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Journal articles on the topic 'Legionnaires' Disease Mathematical models'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Cassell, Kelsie, Paul Gacek, Therese Rabatsky-Ehr, Susan Petit, Matthew Cartter, and Daniel M. Weinberger. "Estimating the True Burden of Legionnaires’ Disease." American Journal of Epidemiology 188, no. 9 (June 21, 2019): 1686–94. http://dx.doi.org/10.1093/aje/kwz142.

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Abstract Over the past decade, the reported incidence of Legionnaires’ disease (LD) in the northeastern United States has increased, reaching 1–3 cases per 100,000 population. There is reason to suspect that this is an underestimate of the true burden, since LD cases may be underdiagnosed. In this analysis of pneumonia and influenza (P&I) hospitalizations, we estimated the percentages of cases due to Legionella, influenza, and respiratory syncytial virus (RSV) by age group. We fitted mixed-effects models to estimate attributable percents using weekly time series data on P&I hospitalizations in Connecticut from 2000 to 2014. Model-fitted values were used to calculate estimates of numbers of P&I hospitalizations attributable to Legionella (and influenza and RSV) by age group, season, and year. Our models estimated that 1.9%, 8.8%, and 5.1% of total (all-ages) inpatient P&I hospitalizations could be attributed to Legionella, influenza, and RSV, respectively. Only 10.6% of total predicted LD cases had been clinically diagnosed as LD during the study period. The observed incidence rate of 1.2 cases per 100,000 population was substantially lower than our estimated rate of 11.6 cases per 100,000 population. Our estimates of numbers of P&I hospitalizations attributable to Legionella are comparable to those provided by etiological studies of community-acquired pneumonia and emphasize the potential for underdiagnosis of LD in clinical settings.

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2

Dobson, A. "Mathematical models for emerging disease." Science 346, no. 6215 (December 11, 2014): 1294–95. http://dx.doi.org/10.1126/science.aaa3441.

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3

Bakshi, Suruchi, Vijayalakshmi Chelliah, Chao Chen, and Piet H. van der Graaf. "Mathematical Biology Models of Parkinson's Disease." CPT: Pharmacometrics & Systems Pharmacology 8, no. 2 (November 2, 2018): 77–86. http://dx.doi.org/10.1002/psp4.12362.

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4

Grassly, Nicholas C., and Christophe Fraser. "Mathematical models of infectious disease transmission." Nature Reviews Microbiology 6, no. 6 (May 13, 2008): 477–87. http://dx.doi.org/10.1038/nrmicro1845.

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5

KLEIN, EILI, RAMANAN LAXMINARAYAN, DAVID L. SMITH, and CHRISTOPHER A. GILLIGAN. "Economic incentives and mathematical models of disease." Environment and Development Economics 12, no. 5 (October 2007): 707–32. http://dx.doi.org/10.1017/s1355770x0700383x.

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The fields of epidemiological disease modeling and economics have tended to work independently of each other despite their common reliance on the language of mathematics and exploration of similar questions related to human behavior and infectious disease. This paper explores the benefits of incorporating simple economic principles of individual behavior and resource optimization into epidemiological models, reviews related research, and indicates how future cross-discipline collaborations can generate more accurate models of disease and its control to guide policy makers.

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Meltzer, M. I., and R. A. I. Norval. "Mathematical models of tick-borne disease transmission." Parasitology Today 9, no. 8 (August 1993): 277–78. http://dx.doi.org/10.1016/0169-4758(93)90116-w.

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7

Donovan, Graham M. "Multiscale mathematical models of airway constriction and disease." Pulmonary Pharmacology & Therapeutics 24, no. 5 (October 2011): 533–39. http://dx.doi.org/10.1016/j.pupt.2011.01.003.

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8

Medley, Graham F. "Mathematical models of tick-borne disease transmission: Reply." Parasitology Today 9, no. 8 (August 1993): 292. http://dx.doi.org/10.1016/0169-4758(93)90123-w.

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9

DUNN, C. E., B. ROWLINGSON, R. S. BHOPAL, and P. DIGGLE. "Meteorological conditions and incidence of Legionnaires' disease in Glasgow, Scotland: application of statistical modelling." Epidemiology and Infection 141, no. 4 (June 12, 2012): 687–96. http://dx.doi.org/10.1017/s095026881200101x.

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SUMMARYThis study investigated the relationships between Legionnaires' disease (LD) incidence and weather in Glasgow, UK, by using advanced statistical methods. Using daily meteorological data and 78 LD cases with known exact date of onset, we fitted a series of Poisson log-linear regression models with explanatory variables for air temperature, relative humidity, wind speed and year, and sine-cosine terms for within-year seasonal variation. Our initial model showed an association between LD incidence and 2-day lagged humidity (positive, P = 0·0236) and wind speed (negative, P = 0·033). However, after adjusting for year-by-year and seasonal variation in cases there were no significant associations with weather. We also used normal linear models to assess the importance of short-term, unseasonable weather values. The most significant association was between LD incidence and air temperature residual lagged by 1 day prior to onset (P = 0·0014). The contextual role of unseasonably high air temperatures is worthy of further investigation. Our methods and results have further advanced understanding of the role which weather plays in risk of LD infection.

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10

De Gaetano, Andrea, Thomas Hardy, Benoit Beck, Eyas Abu-Raddad, Pasquale Palumbo, Juliana Bue-Valleskey, and Niels Pørksen. "Mathematical models of diabetes progression." American Journal of Physiology-Endocrinology and Metabolism 295, no. 6 (December 2008): E1462—E1479. http://dx.doi.org/10.1152/ajpendo.90444.2008.

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Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.

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11

Cabanlit, Epimaco A., Elsie M. Cabanlit, Steiltjes M. Cabanlit, and Roxan Eve M. Cabanlit. "Mathematical Models for the Coronavirus Disease (Covid-19) Pandemic." International Journal of Scientific and Research Publications (IJSRP) 10, no. 4 (April 24, 2020): p10082. http://dx.doi.org/10.29322/ijsrp.10.04.2020.p10082.

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12

COEN, P. G., P. T. HEATH, M. L. BARBOUR, and G. P. GARNETT. "Mathematical models of Haemophilus influenzae type b." Epidemiology and Infection 120, no. 3 (June 1998): 281–95. http://dx.doi.org/10.1017/s0950268898008784.

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A review of empirical studies and the development of a simple theoretical framework are used to explore the relationship between Haemophilus influenzae type b (Hib) carriage and disease within populations. The models emphasize the distinction between asymptomatic and symptomatic infection. Maximum likelihood methods are used to estimate parameter values of the models and to evaluate whether models of infection and disease are satisfactory. The low incidence of carriage suggests that persistence of infection is only compatible with the absence of acquired immunity to asymptomatic infection. The slight decline in carriage rates amongst adults is compatible with acquired immunity, but could be a consequence of reduced contacts. The low rate of disease observed in adulthood cannot be explained if protection from disease is a product of previous detectable exposure to Hib alone. We estimate an Ro of 3·3 for Hib in developed countries, which suggests that current immunization programmes may eliminate the infection. Analysis of the disease data set suggests the absence of maternal immunity and increased susceptibility to disease in the oldest age classes.

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13

Curcio, Luciano, Laura D'Orsi, and Andrea De Gaetano. "Seven Mathematical Models of Hemorrhagic Shock." Computational and Mathematical Methods in Medicine 2021 (June 3, 2021): 1–34. http://dx.doi.org/10.1155/2021/6640638.

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Although mathematical modelling of pressure-flow dynamics in the cardiocirculatory system has a lengthy history, readily finding the appropriate model for the experimental situation at hand is often a challenge in and of itself. An ideal model would be relatively easy to use and reliable, besides being ethically acceptable. Furthermore, it would address the pathogenic features of the cardiovascular disease that one seeks to investigate. No universally valid model has been identified, even though a host of models have been developed. The object of this review is to describe several of the most relevant mathematical models of the cardiovascular system: the physiological features of circulatory dynamics are explained, and their mathematical formulations are compared. The focus is on the whole-body scale mathematical models that portray the subject’s responses to hypovolemic shock. The models contained in this review differ from one another, both in the mathematical methodology adopted and in the physiological or pathological aspects described. Each model, in fact, mimics different aspects of cardiocirculatory physiology and pathophysiology to varying degrees: some of these models are geared to better understand the mechanisms of vascular hemodynamics, whereas others focus more on disease states so as to develop therapeutic standards of care or to test novel approaches. We will elucidate key issues involved in the modeling of cardiovascular system and its control by reviewing seven of these models developed to address these specific purposes.

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14

Dike, Chinyere Ogochukwu, Zaitul Marlizawati Zainuddin, and Ikeme John Dike. "Mathematical Models for Mitigating Ebola Virus Disease Transmission: A Review." Advanced Science Letters 24, no. 5 (May 1, 2018): 3536–43. http://dx.doi.org/10.1166/asl.2018.11432.

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15

Feinstein, A. R., C. K. Chan, J. M. Esdaile, R. I. Horwitz, M. J. McFarlane, and C. K. Wells. "Mathematical models and scientific reality in occurrence rates for disease." American Journal of Public Health 79, no. 9 (September 1989): 1303–4. http://dx.doi.org/10.2105/ajph.79.9.1303.

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16

Black, F. L., and B. Singer. "Elaboration Versus Simplification in Refining Mathematical Models of Infectious Disease." Annual Review of Microbiology 41, no. 1 (October 1987): 677–701. http://dx.doi.org/10.1146/annurev.mi.41.100187.003333.

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17

Garnett, G. P. "An introduction to mathematical models in sexually transmitted disease epidemiology." Sexually Transmitted Infections 78, no. 1 (February 1, 2002): 7–12. http://dx.doi.org/10.1136/sti.78.1.7.

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18

Sarbaz, Yashar, and Hakimeh Pourakbari. "A review of presented mathematical models in Parkinson’s disease: black- and gray-box models." Medical & Biological Engineering & Computing 54, no. 6 (November 7, 2015): 855–68. http://dx.doi.org/10.1007/s11517-015-1401-9.

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19

Weerasinghe, Hasitha N., Pamela M. Burrage, Kevin Burrage, and Dan V. Nicolau. "Mathematical Models of Cancer Cell Plasticity." Journal of Oncology 2019 (October 31, 2019): 1–14. http://dx.doi.org/10.1155/2019/2403483.

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Quantitative modelling is increasingly important in cancer research, helping to integrate myriad diverse experimental data into coherent pictures of the disease and able to discriminate between competing hypotheses or suggest specific experimental lines of enquiry and new approaches to therapy. Here, we review a diverse set of mathematical models of cancer cell plasticity (a process in which, through genetic and epigenetic changes, cancer cells survive in hostile environments and migrate to more favourable environments, respectively), tumour growth, and invasion. Quantitative models can help to elucidate the complex biological mechanisms of cancer cell plasticity. In this review, we discuss models of plasticity, tumour progression, and metastasis under three broadly conceived mathematical modelling techniques: discrete, continuum, and hybrid, each with advantages and disadvantages. An emerging theme from the predictions of many of these models is that cell escape from the tumour microenvironment (TME) is encouraged by a combination of physiological stress locally (e.g., hypoxia), external stresses (e.g., the presence of immune cells), and interactions with the extracellular matrix. We also discuss the value of mathematical modelling for understanding cancer more generally.

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20

Hughes, G. "Validating mathematical models of plant-disease progress in space and time." Mathematical Medicine and Biology 14, no. 2 (June 1, 1997): 85–112. http://dx.doi.org/10.1093/imammb/14.2.85.

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21

Fujiwara, Takeo. "Mathematical Analysis of Epidemic Disease Models and Application to COVID-19." Journal of the Physical Society of Japan 90, no. 2 (February 15, 2021): 023801. http://dx.doi.org/10.7566/jpsj.90.023801.

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22

Florea, Aurelia, and Cristian Lăzureanu. "A mathematical model of infectious disease transmission." ITM Web of Conferences 34 (2020): 02002. http://dx.doi.org/10.1051/itmconf/20203402002.

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In this paper we consider a three-dimensional nonlinear system which models the dynamics of a population during an epidemic disease. The considered model is a SIS-type system in which a recovered individual automatically becomes a susceptible one. We take into account the births and deaths, and we also consider that susceptible individuals are divided into two groups: non-vaccinated and vaccinated. In addition, we assume a medical scenario in which vaccinated people take a special measure to quarantine their newborns. We study the stability of the considered system. Numerical simulations point out the behavior of the considered population.

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23

Weir, Mark H., Alexis L. Mraz, and Jade Mitchell. "An Advanced Risk Modeling Method to Estimate Legionellosis Risks Within a Diverse Population." Water 12, no. 1 (December 20, 2019): 43. http://dx.doi.org/10.3390/w12010043.

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Quantitative microbial risk assessment (QMRA) is a computational science leveraged to optimize infectious disease controls at both population and individual levels. Often, diverse populations will have different health risks based on a population’s susceptibility or outcome severity due to heterogeneity within the host. Unfortunately, due to a host homogeneity assumption in the microbial dose-response models’ derivation, the current QMRA method of modeling exposure volume heterogeneity is not an accurate method for pathogens such as Legionella pneumophila. Therefore, a new method to model within-group heterogeneity is needed. The method developed in this research uses USA national incidence rates from the Centers for Disease Control and Prevention (CDC) to calculate proxies for the morbidity ratio that are descriptive of the within-group variability. From these proxies, an example QMRA model is developed to demonstrate their use. This method makes the QMRA results more representative of clinical outcomes and increases population-specific precision. Further, the risks estimated demonstrate a significant difference between demographic groups known to have heterogeneous health outcomes after infection. The method both improves fidelity to the real health impacts resulting from L. pneumophila infection and allows for the estimation of severe disability-adjusted life years (DALYs) for Legionnaires’ disease, moderate DALYs for Pontiac fever, and post-acute DALYs for sequela after recovering from Legionnaires’ disease.

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24

Bravo de la Parra, R., M. Marvá, E. Sánchez, and L. Sanz. "Discrete Models of Disease and Competition." Discrete Dynamics in Nature and Society 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/5310837.

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The aim of this work is to analyze the influence of the fast development of a disease on competition dynamics. To this end we present two discrete time ecoepidemic models. The first one corresponds to the case of one parasite affecting demography and intraspecific competition in a single host, whereas the second one contemplates the more complex case of competition between two different species, one of which is infected by the parasite. We carry out a complete mathematical analysis of the asymptotic behavior of the solutions of the corresponding systems of difference equations and derive interesting ecological information about the influence of a disease in competition dynamics. This includes an assessment of the impact of the disease on the equilibrium population of both species as well as some counterintuitive behaviors in which although we would expect the outbreak of the disease to negatively affect the infected species, the contrary happens.

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25

El Khatib, N., O. Kafi, A. Sequeira, S. Simakov, Yu Vassilevski, and V. Volpert. "Mathematical modelling of atherosclerosis." Mathematical Modelling of Natural Phenomena 14, no. 6 (2019): 603. http://dx.doi.org/10.1051/mmnp/2019050.

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The review presents the state of the art in the atherosclerosis modelling. It begins with the biological introduction describing the mechanisms of chronic inflammation of artery walls characterizing the development of atherosclerosis. In particular, we present in more detail models describing this chronic inflammation as a reaction-diffusion wave with regimes of propagation depending on the level of cholesterol (LDL) and models of rolling monocytes initializing the inflammation. Further development of this disease results in the formation of atherosclerotic plaque, vessel remodelling and possible plaque rupture due its interaction with blood flow. We review plaque-flow interaction models as well as reduced models (0D and 1D) of blood flow in atherosclerotic vasculature.

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26

Yanchevskaya, E. Ya, and O. A. Mesnyankina. "Mathematical Modelling and Prediction in Infectious Disease Epidemiology." RUDN Journal of Medicine 23, no. 3 (December 15, 2019): 328–34. http://dx.doi.org/10.22363/2313-0245-2019-23-3-328-334.

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Mathematical modeling of diseases is an urgent problem in the modern world. More and more researchers are turning to mathematical models to predict a particular disease, as they help the most correct and accurate study of changes in certain processes occurring in society. Mathematical modeling is indispensable in certain areas of medicine, where real experiments are impossible or difficult, for example, in epidemiology. The article is devoted to the historical aspects of studying the possibilities of mathematical modeling in medicine. The review demonstrates the main stages of development, achievements and prospects of this direction.

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27

Langemann, Dirk, Igor Nesteruk, and Jürgen Prestin. "Comparison of mathematical models for the dynamics of the Chernivtsi children disease." Mathematics and Computers in Simulation 123 (May 2016): 68–79. http://dx.doi.org/10.1016/j.matcom.2016.01.003.

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28

Roberts, Paul A., Eamonn A. Gaffney, Philip J. Luthert, Alexander J. E. Foss, and Helen M. Byrne. "Mathematical and computational models of the retina in health, development and disease." Progress in Retinal and Eye Research 53 (July 2016): 48–69. http://dx.doi.org/10.1016/j.preteyeres.2016.04.001.

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29

Durham, David P., and Elizabeth A. Casman. "Incorporating individual health-protective decisions into disease transmission models: a mathematical framework." Journal of The Royal Society Interface 9, no. 68 (July 20, 2011): 562–70. http://dx.doi.org/10.1098/rsif.2011.0325.

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It is anticipated that the next generation of computational epidemic models will simulate both infectious disease transmission and dynamic human behaviour change. Individual agents within a simulation will not only infect one another, but will also have situational awareness and a decision algorithm that enables them to modify their behaviour. This paper develops such a model of behavioural response, presenting a mathematical interpretation of a well-known psychological model of individual decision making, the health belief model, suitable for incorporation within an agent-based disease-transmission model. We formalize the health belief model and demonstrate its application in modelling the prevalence of facemask use observed over the course of the 2003 Hong Kong SARS epidemic, a well-documented example of behaviour change in response to a disease outbreak.

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30

Liu, Yifan. "Mathematical models of vaccine inventory design for a breakout of epidemic disease." PAMM 7, no. 1 (December 2007): 2150013–14. http://dx.doi.org/10.1002/pamm.200700367.

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31

Nkeki, C. I., and G. O. S. Ekhaguere. "Some actuarial mathematical models for insuring the susceptibles of a communicable disease." International Journal of Financial Engineering 07, no. 02 (May 18, 2020): 2050014. http://dx.doi.org/10.1142/s2424786320500140.

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Using epidemiological and actuarial analysis, this paper formulates some new actuarial mathematical models, called S-I-DR-S models, for insuring the susceptibles of a population exposed to a communicable disease. Epidemiologically, the population is structured into four demographic groups, namely: susceptibles [Formula: see text], infectives [Formula: see text], diseased [Formula: see text] and recovered [Formula: see text], with the latter automatically re-entering the group of susceptibles [Formula: see text]. The insurance policies are targeted at the members of the susceptible group who face the risk of infection and death due to the disease. Using actuarial techniques and principles, we determine some interesting features of the model, namely, (a) financial obligations of the parties, (b) present value of premiums, (c) quantum of claims by infected policy holders (PHs), (d) quantum of claims on behalf of deceased PHs, (e) cumulative insurance reserve for annuity and (f) lump sum plan. To check the risk of insolvency, premium adjustment for the PHs is also considered.

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32

FENTON, ANDY. "Editorial: Mathematical modelling of infectious diseases." Parasitology 143, no. 7 (March 30, 2016): 801–4. http://dx.doi.org/10.1017/s0031182016000214.

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The field of disease ecology – the study of the spread and impact of parasites and pathogens within their host populations and communities – has a long history of using mathematical models. Dating back over 100 years, researchers have used mathematics to describe the spread of disease-causing agents, understand the relationship between host density and transmission and plan control strategies. The use of mathematical modelling in disease ecology exploded in the late 1970s and early 1980s through the work of Anderson and May (Anderson and May, 1978, 1981, 1992; May and Anderson, 1978), who developed the fundamental frameworks for studying microparasite (e.g. viruses, bacteria and protozoa) and macroparasite (e.g. helminth) dynamics, emphasizing the importance of understanding features such as the parasite's basic reproduction number (R0) and critical community size that form the basis of disease ecology research to this day. Since the initial models of disease population dynamics, which primarily focused on human diseases, theoretical disease research has expanded hugely to encompass livestock and wildlife disease systems, and also to explore evolutionary questions such as the evolution of parasite virulence or drug resistance. More recently there have been efforts to broaden the field still further, to move beyond the standard ‘one-host-one-parasite’ paradigm of the original models, to incorporate many aspects of complexity of natural systems, including multiple potential host species and interactions among multiple parasite species.

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33

El Khatib, N., S. Génieys, B. Kazmierczak, and V. Volpert. "Mathematical modelling of atherosclerosis as an inflammatory disease." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1908 (December 13, 2009): 4877–86. http://dx.doi.org/10.1098/rsta.2009.0142.

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Atherosclerosis is an inflammatory disease. The atherosclerosis process starts when low-density lipoproteins (LDLs) enter the intima of the blood vessel, where they are oxidized (ox-LDLs). The anti-inflammatory response triggers the recruitment of monocytes. Once in the intima, the monocytes are transformed into macrophages and foam cells, leading to the production of inflammatory cytokines and further recruitment of monocytes. This auto-amplified process leads to the formation of an atherosclerotic plaque and, possibly, to its rupture. In this paper we develop two mathematical models based on reaction–diffusion equations in order to explain the inflammatory process. The first model is one-dimensional: it does not consider the intima’s thickness and shows that low ox-LDL concentrations in the intima do not lead to a chronic inflammatory reaction. Intermediate ox-LDL concentrations correspond to a bistable system, which can lead to a travelling wave that can be initiated by certain conditions, such as infection or injury. High ox-LDL concentrations correspond to a monostable system, and even a small perturbation of the non-inflammatory case leads to travelling-wave propagation, which corresponds to a chronic inflammatory response. The second model we suggest is two-dimensional: it represents a reaction–diffusion system in a strip with nonlinear boundary conditions to describe the recruitment of monocytes as a function of the cytokines’ concentration. We prove the existence of travelling waves and confirm our previous results, which show that atherosclerosis develops as a reaction–diffusion wave. The results of the two models are confirmed by numerical simulations. The latter show that the two-dimensional model converges to the one-dimensional one if the thickness of the intima tends to zero.

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Michor, Franziska. "Mathematical Models of Cancer Evolution and Cure." Blood 126, no. 23 (December 3, 2015): SCI—54—SCI—54. http://dx.doi.org/10.1182/blood.v126.23.sci-54.sci-54.

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Abstract Since the pioneering work of Salmon and Durie, the availability of a quantitative measure of malignant cell burden in multiple myeloma has been used to make clinical predictions and to model tumor cell growth. Here, we analyzed a large set of tumor response data from three randomized controlled clinical trials (total sample size n=1,469 evaluable patients) to establish and validate a novel mathematical model of MM cell dynamics based on responses to bortezomib-based chemotherapy regimens. Dynamics of treatment response in newly diagnosed patients were most consistent with a mathematical model postulating the existence of two tumor cell subpopulations, "myeloma progenitor cells" and "myeloma differentiated cells". Differential treatment responses were observed with significant tumoricidal effects on myeloma differentiated cells and less clear effects on myeloma progenitor cells. We validated this model using a second trial of newly diagnosed MM patients and a third trial of refractory patients. When applying our model to data of relapsed MM patients, we found that a hybrid mathematical model incorporating both a MM differentiation hierarchy and clonal evolution best explains the tumor response patterns in all patients. The clinical data, together with mathematical modeling, suggest that bortezomib-based therapy exerts a selection pressure on myeloma cells that can shape the disease phenotype, thereby generating further inter-patient variability. This model may be a useful tool for improving the rational design of chemotherapy regimens in multiple myeloma. Disclosures No relevant conflicts of interest to declare.

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Goncharova, Anastaciya B., Eugeny P. Kolpak, Madina M. Rasulova, and Alina V. Abramova. "Mathematical modeling of cancer treatment." Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 16, no. 4 (2020): 437–46. http://dx.doi.org/10.21638/11701/spbu10.2020.408.

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The paper proposes mathematical models of ovarian neoplasms. The models are based on a mathematical model of interference competition. Two types of cells are involved in the competition for functional space: normal and tumor cells. The mathematical interpretation of the models is the Cauchy problem for a system of ordinary differential equations. The dynamics of tumor growth is determined on the basis of the model. A model for the distribution of conditional patients according to four stages of the disease, a model for assessing survival times for groups of conditional patients, and a chemotherapy model are also proposed.

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VAN HEST, N. A. H., C. J. P. A. HOEBE, J. W. DEN BOER, J. K. VERMUNT, E. P. F. IJZERMAN, W. G. BOERSMA, and J. H. RICHARDUS. "Incidence and completeness of notification of Legionnaires' disease in The Netherlands: covariate capture–recapture analysis acknowledging regional differences." Epidemiology and Infection 136, no. 4 (June 22, 2007): 540–50. http://dx.doi.org/10.1017/s0950268807008977.

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SUMMARYTo estimate incidence and completeness of notification of Legionnaires' disease (LD) in The Netherlands in 2000 and 2001, we performed a capture–recapture analysis using three registers: Notifications, Laboratory results and Hospital admissions. After record-linkage, 373 of the 780 LD patients identified were notified. Ascertained under-notification was 52·2%. Because of expected and observed regional differences in the incidence rate of LD, alternatively to conventional log-linear capture–recapture models, a covariate (region) capture–recapture model, not previously used for estimating infectious disease incidence, was specified and estimated 886 LD patients (95% confidence interval 827–1022). Estimated under-notification was 57·9%. Notified, ascertained and estimated average annual incidence rates of LD were 1·15, 2·42 and 2·77/100 000 inhabitants respectively, with the highest incidence in the southern region of The Netherlands. Covariate capture–recapture analysis acknowledging regional differences of LD incidence appears to reduce bias in the estimated national incidence rate.

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Chung, Chun Yen, Hung Yuan Chung, and Wen Tsai Sung. "Mathematical Models for the Dynamics Simulation of Tuberculosis." Applied Mechanics and Materials 418 (September 2013): 265–68. http://dx.doi.org/10.4028/www.scientific.net/amm.418.265.

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In recent years, following malaria, tuberculosis, AIDS, Novel Influenza, and other infectious diseases, have an enormous impact on the entire globe, and directly and profoundly awaken the public, making them cognitive and alert regarding emerging and re-emerging infectious diseases. For some countries or developing regions, tuberculosis is still very serious, however, the public is still unclear TB development and change a variety of factors, therefore, need a model theory of tuberculosis. In view of this, the global epidemic, scientists and statisticians hope to further develop a complete inspection and data acquisition system and is committed to the existing monitoring system, and through the establishment of mathematical models and the spread of infectious diseases dynamics of quantitative methods to facilitate the practical application and control of epidemics, trends and cost-benefit assessment, and help build disease prevention policies, evaluation and revision.

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Shain, Kenneth H. "Mathematical Models of Cancer Evolution and Cure." Blood 126, no. 23 (December 3, 2015): SCI—55—SCI—55. http://dx.doi.org/10.1182/blood.v126.23.sci-55.sci-55.

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You cannot cure what you do not understand. So how can mathematical modeling address this pressing issue? The advances in therapeutic success in multiple myeloma over the last decades have hinged on an an army of researchers identifying a critical genetic, epigenetic and biochemical signaling factors within of MM cells as well as the tumor microenvironment (TME). Unfortunately, despite these large scale efforts we do not yet offer our patients curative intent therapy. The inability to provide curative therapy, especially in the setting of HRMM, is characterized by evolving resistance to lines of sequential therapy as a result of alternating clonal dynamics following the failure of initial therapy to eradicate minimal residual disease (MRD). Recent results underline the importance of tumor heterogeneity, in the form of pre-existing genotypically (and phenotypically) distinct sub-populations that translate to drug-resistant phenotypes leading to treatment failure. This phenomenon of “clonal tides”, has been well characterized using contemporary molecular techniques demonstrating that clonal evolution progresses by different evolutionary patterns across patients. Thus, resistance to therapy is a consequence of Darwinian dynamics- influenced by tumor heterogeneity, genomic instability, the TME (ecosystem), and selective pressures induced by therapy. Such evolutionary principles can be analyzed and exploited by mathematical models to personalize therapeutic options for patients with MM. Currently available clinical decision support tools and physician acumen are not able to account for the shear amount of information available. Mathematical models, however, provide a critical mechanism(s) to account of the large number of aspects to help predict and manage MM- accounting for what we do not know. Models can be designed with the specific intent of characterizing intra-tumoral heterogeneity, changing ecosystems, and clinical parameters over time to create patient-specific clinical predictions much like hurricane prediction models. This can only be achieved by creating mathematical models parameterized by longitudinal data of a number of parameters. The novel application of mathematical models based on Darwinian dynamics can be imputed with data to 1) predict progression events (risk of progression to from smoldering to active MM), 2) relapse, and 3) predictions of clinical response of MM patients for the optimizing therapeutics for cure or optimal control of MM; thus, providing invaluable clinical decision support tools. Disclosures: Shain: Celgene: Consultancy , Speakers Bureau ; Amgen/Onyx: Consultancy , Speakers Bureau ; Takeda: Consultancy , Speakers Bureau ; Signal Genetics: Consultancy , Research Funding.

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Brownell, A. L., B. G. Jenkins, and O. Isacson. "Dopamine imaging markers and predictive mathematical models for progressive degeneration in Parkinson's disease." Biomedicine & Pharmacotherapy 53, no. 3 (April 1999): 131–40. http://dx.doi.org/10.1016/s0753-3322(99)80078-x.

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Chowell, G. "Mathematical models to elucidate the transmission dynamics and control of vector-borne disease." International Journal of Infectious Diseases 53 (December 2016): 6–7. http://dx.doi.org/10.1016/j.ijid.2016.11.020.

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Jäger, Jens, Sebastian Marwitz, Jana Tiefenau, Janine Rasch, Olga Shevchuk, Christian Kugler, Torsten Goldmann, and Michael Steinert. "Human Lung Tissue Explants Reveal Novel Interactions during Legionella pneumophila Infections." Infection and Immunity 82, no. 1 (October 28, 2013): 275–85. http://dx.doi.org/10.1128/iai.00703-13.

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ABSTRACTHistological and clinical investigations describe late stages of Legionnaires' disease but cannot characterize early events of human infection. Cellular or rodent infection models lack the complexity of tissue or have nonhuman backgrounds. Therefore, we developed and applied a novel model forLegionella pneumophilainfection comprising living human lung tissue. We stimulated lung explants withL. pneumophilastrains and outer membrane vesicles (OMVs) to analyze tissue damage, bacterial replication, and localization as well as the transcriptional response of infected tissue. Interestingly, we found that extracellular adhesion ofL. pneumophilato the entire alveolar lining precedes bacterial invasion and replication in recruited macrophages. In contrast, OMVs predominantly bound to alveolar macrophages. Specific damage to septa and epithelia increased over 48 h and was stronger in wild-type-infected and OMV-treated samples than in samples infected with the replication-deficient, type IVB secretion-deficient DotA−strain. Transcriptome analysis of lung tissue explants revealed a differential regulation of 2,499 genes after infection. The transcriptional response included the upregulation of uteroglobin and the downregulation of the macrophage receptor with collagenous structure (MARCO). Immunohistochemistry confirmed the downregulation of MARCO at sites of pathogen-induced tissue destruction. Neither host factor has ever been described in the context ofL. pneumophilainfections. This work demonstrates that the tissue explant model reproduces realistic features of Legionnaires' disease and reveals new functions for bacterial OMVs during infection. Our model allows us to characterize early steps of human infection which otherwise are not feasible for investigations.

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Tchuenche, Jean M. "Patient-dependent effects in disease control: a mathematical model." ANZIAM Journal 48, no. 4 (April 2007): 583–96. http://dx.doi.org/10.1017/s1446181100003230.

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AbstractThe state of a patient is an important concept in biomedical sciences. While analytical methods for predicting and exploring treatment strategies of disease dynamics have proven to have useful applications in public health policy and planning, the state of a patient has attracted less attention, at least mathematically. As a result, models constructed in relation to treatment strategies may not be very informative. We derive a patient-dependent parameter from an age-physiology dependent population model, and show that a single treatment strategy is not always optimal. Also, we derive a function which increases with the patient dependence parameter and describes the effort expended to be in good health.

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Rodriguez-Brenes, Ignacio A., and Dominik Wodarz. "Preventing clonal evolutionary processes in cancer: Insights from mathematical models." Proceedings of the National Academy of Sciences 112, no. 29 (July 21, 2015): 8843–50. http://dx.doi.org/10.1073/pnas.1501730112.

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Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.

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Ishtiaq, Amna. "Dynamics of COVID-19 Transmission: Compartmental-based Mathematical Modeling." Life and Science 1, supplement (December 23, 2020): 5. http://dx.doi.org/10.37185/lns.1.1.134.

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The current pandemic of coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-Cov2) demands scientists all over the world to make their possible contributions in whatever way possible to control this disease. In such health emergency, mathematical epidemiologists are playing a pivotal role by constructing different mathematical and statistical models for predicting different future scenario and their impact on different intervention strategies to policy makers and health legislators. Compartmental-based models (CBM), are a type of transmission dynamic framework, which are one of the most studied models during this pandemic. This communication highlights the role CBM models play for the understanding of COVID-19 transmission dynamics.

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FORYS, URSULA. "INTERLEUKIN MATHEMATICAL MODEL OF AN IMMUNE SYSTEM." Journal of Biological Systems 03, no. 03 (September 1995): 889–902. http://dx.doi.org/10.1142/s0218339095000794.

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Some generalizations of Marchuk's model of an infectious disease with respect to the role of interleukins are presented in this paper. Basic properties of the models are studied. Results of numerical simulations with different coefficients corresponding to the different forms of the disease are shown.

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Christen, Paula, and Lesong Conteh. "How are mathematical models and results from mathematical models of vaccine-preventable diseases used, or not, by global health organisations?" BMJ Global Health 6, no. 9 (September 2021): e006827. http://dx.doi.org/10.1136/bmjgh-2021-006827.

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While epidemiological and economic evidence has the potential to provide answers to questions, guide complex programmes and inform resource allocation decisions, how this evidence is used by global health organisations who commission it and what organisational actions are generated from the evidence remains unclear. This study applies analytical tools from organisational science to understand how evidence produced by infectious disease epidemiologists and health economists is used by global health organisations. A conceptual framework that embraces evidence use typologies and relates findings to the organisational process of action generation informs and structures the research. Between March and September 2020, we conducted in-depth interviews with mathematical modellers (evidence producers) and employees at global health organisations, who are involved in decision-making processes (evidence consumers). We found that commissioned epidemiological and economic evidence is used to track progress and provides a measure of success, both in terms of health outcomes and the organisations’ mission. Global health organisations predominantly use this evidence to demonstrate accountability and solicit funding from external partners. We find common understanding and awareness across consumers and producers about the purposes and uses of these commissioned pieces of work and how they are distinct from more academic explorative research outputs. Conceptual evidence use best describes this process. Evidence is slowly integrated into organisational processes and is one of many influences on global health organisations’ actions. Relationships developed over time and trust guide the process, which may lead to quite a concentrated cluster of those producing and commissioning models. These findings raise several insights relevant to the literature of research utilisation in organisations and evidence-based management. The study extends our understanding of how evidence is used and which organisational actions are generated as a result of commissioning epidemiological and economic evidence.

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Bowong, S., A. Temgoua, Y. Malong, and J. Mbang. "Mathematical Study of a Class of Epidemiological Models with Multiple Infectious Stages." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 3-4 (May 26, 2020): 259–74. http://dx.doi.org/10.1515/ijnsns-2017-0244.

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AbstractThis paper deals with the mathematical analysis of a general class of epidemiological models with multiple infectious stages for the transmission dynamics of a communicable disease. We provide a theoretical study of the model. We derive the basic reproduction number $\mathcal R_0$ that determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever $\mathcal R_0 \leq 1$, while when $\mathcal R_0 \gt 1$, the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. A case study for tuberculosis (TB) is considered to numerically support the analytical results.

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Дерпак, V. Derpak, Полухин, V. Polukhin, Еськов, Valeriy Eskov, Пашнин, and A. Pashnin. "Mathematical modeling of involuntary movements in health and disease." Complexity. Mind. Postnonclassic 4, no. 2 (September 25, 2015): 75–86. http://dx.doi.org/10.12737/12002.

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The problem of voluntary or involuntary movements are discussed more than 150 years. Traditionally, the tremor was considered involuntary movements and tapping - arbitrary. Real stochastic and chaotic analysis of these two types of motion shows them as chaotic motion (involuntary as a result of the test, rather than by the presence of the target). Introduced new criteria for the separation of these two types of motion in the form of paired comparisons matrix samples tremorogramm and teppingramm. Models of the evolution of the tremor in the mode of the three transitions: normal postural tremor, tremor in Parkinson´s disease and the transition to a rigid form of the disease. A comparison of model data and observations on patients. In addition, it is proposed dimensioning of quasi-attractors of these two types of movements, which provide the identification of differences of physiological state of the subject. Demonstrated specific examples of parameters matrix of paired comparisons and quasi-attractors while perturbation the final test.

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Chowdhury, Debashish, and Dietrich Stauffer. "Systematics of the models of immune response and autoimmune disease." Journal of Statistical Physics 59, no. 3-4 (May 1990): 1019–42. http://dx.doi.org/10.1007/bf01025860.

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Miller, Joel C. "Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes." Infectious Disease Modelling 2, no. 1 (February 2017): 35–55. http://dx.doi.org/10.1016/j.idm.2016.12.003.

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