Academic literature on the topic 'Susceptible-Infected-Susceptible (SIS) model'

We study the evolution of degree distributions of susceptible-infected-susceptible (SIS) model on random networks, where susceptible nodes are capable of being infected, and infected nodes can spread the disease further. The network of contacts is modeled as a configuration model featuring heterogeneous degree distribution. We derive systematically the (excess) degree distributions among susceptible and infected individuals by using the probability generating function formalism.

This paper studies a time-varyingSIS(i.e.containing susceptible and infected populations) propagation disease model exhibiting a nonlinear incidence rate and impulsive eventual culling of both populations so that the individuals recover with no immunity to the disease. The nonlinear incidence rate consists of two time-varying additive terms proportional to the susceptible and infected populations normalized to the total population.

A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper. We introduce the basic reproduction number [Formula: see text] first. Then the existence of endemic equilibrium (EE) can be determined by the sizes of [Formula: see text] as well as the diffusion rates of susceptible and infected individuals. We also investigate the effect of diffusion rates on asymptotic profile of EE. Our results conclude that the infected population will die out if the diffusion rate of susceptible individuals is small and the total population [Formula: see text] is below a certain level; while the two populations persist eventually if at least one of the diffusion rates of the susceptible and infected individuals is large.

<abstract><p>This article is concerned with the determination of the diffusion matrix in the reaction-diffusion mathematical model arising from the spread of an epidemic. The mathematical model that we consider is a susceptible-infected-susceptible model with diffusion, which was deduced by assuming the following hypotheses: The total population can be partitioned into susceptible and infected individuals; a healthy susceptible individual becomes infected through contact with an infected individual; there is no immunity, and infected individuals can become susceptible again; the spread of epidemics arises in a spatially heterogeneous environment; the susceptible and infected individuals implement strategies to avoid each other by staying away. The spread of the dynamics is governed by an initial boundary value problem for a reaction-diffusion system, where the model unknowns are the densities of susceptible and infected individuals and the boundary condition models the fact that there is neither emigration nor immigration through their boundary. The reaction consists of two terms modeling disease transmission and infection recovery, and the diffusion is a space-dependent full diffusion matrix. The determination of the diffusion matrix was conducted by considering that we have experimental data on the infective and susceptible densities at some fixed time and in the overall domain where the population lives. We reformulated the identification problem as an optimal control problem where the cost function is a regularized least squares function. The fundamental contributions of this article are the following: The existence of at least one solution to the optimization problem or, equivalently, the diffusion identification problem; the introduction of first-order necessary optimality conditions; and the necessary conditions that imply a local uniqueness result of the inverse problem. In addition, we considered two numerical examples for the case of parameter identification.</p></abstract>

The paper analyzes the influence of a susceptible–infectious–susceptible (SIS) infectious disease affecting both fish and broiler species. The paper also considers a joint SIS project of fish and broiler in which the growth rates of both species vary with available nutrients and environmental carrying capacities of biomasses. The nutrients for both species are functions of the biomasses of the two species. The harvesting rates of fish and broiler depend linearly on common effort function. It is assumed that the diseases are transmitted to the susceptible populations by direct contact with the infected populations. Using the medicine, some portion of the infected populations are transmitted to the susceptible populations. The existence of steady states and their stability are investigated analytically. The joint profit of the SIS model is maximized using Pontryagin’s maximum principle and corresponding optimum harvesting rates are also obtained. Using Mathematica software, the models are illustrated and the optimum results are obtained and presented in tabular and graphical forms.

The effect of partial isolation has been studied in disease spreading processes using the framework of susceptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) models. The partial isolation is introduced by imposing a restriction: each infected individual can probabilistically infect up to a maximum number n of his susceptible neighbors, but not all. It has been observed that the critical values of the spreading rates for endemic states are non-zero in both models and decrease as 1/n with n, on all graphs including scale-free graphs. In particular, the SIR model with n = 2 turned out to be a special case, characterized by a new bond percolation threshold on square lattice.

This work presents a stochastic model of malaria spread. We first calculated the basic reproduction number R0 of the models ShIhRhSh‐SvIv and ShLhIhRhSh‐SvLvIv in order to show that the malaria-free equilibrium is asymptotically stable; then, we used a finite Markov chain model to describe the interactions between the different compartments of the model SeLeIeReSe‐SaLaIaRaSa‐SvIv. We carried out numerical simulations of our results for two types of transmission zones: a zone with low malaria transmission and an endemic zone. Through these simulations, we first determined the invariant stationary distribution π∗ of the model, and then, we found that the use of the indoor residual spraying (IRS) method by regular application of insecticides is more effective for the elimination of malaria than the use of long-acting impregnated mosquito nets (LLINs).

Due to the fact that the “nodes” and “links” of real networks are heterogeneous, to model computer viruses prevalence throughout the Internet, we borrow the idea of the reduced scale free network which was introduced recently. The purpose of this paper is to extend the previous deterministic two subchains of Susceptible-Infected-Susceptible (SIS) model into a mixed Susceptible-Infected-Recovered and Susceptible-Infected-Susceptible (SIR–SIS) model to contain the computer virus spreading over networks with two degrees. Moreover, we develop its stochastic counterpart. Due to the high protection and security taken for hubs class, we suggest to treat it by using SIR epidemic model rather than the SIS one. The analytical study reveals that the proposed model admits a stable viral equilibrium. Thus, it is shown numerically that the mean dynamic behavior of the stochastic model is in agreement with the deterministic one. Unlike the infection densities [Formula: see text] and [Formula: see text] which both tend to a viral equilibrium for both approaches as in the previous study, [Formula: see text] tends to the virus-free equilibrium. Furthermore, since a proportion of infectives are recovered, the global infection density [Formula: see text] is minimized. Therefore, the permanent presence of viruses in the network due to the lower-degree nodes class. Many suggestions are put forward for containing viruses propagation and minimizing their damages.

We examine the interplay of motility and information exchange in a model of active particles. Non-motile particles additionally recover their motility at a fixed rate, as in the SIS (Susceptible, Infected, Susceptible) model of epidemic spreading.

In this paper, we explore the long time behavior of a multigroup Susceptible–Infected–Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.

Cette thèse explore la prise de décision décentralisée dans les dynamiques épidémiques et de marketing viral en utilisant la théorie des jeux afin d'évaluer son efficacité. La thèse commence par une revue des outils mathématiques, mettant l'accent sur la théorie des graphes/jeux. Dans la suite de ce manuscrit, l'analyse de jeu épidémiologique et de compétition en marketing viral est établie. Notamment, dans le chapitre 2 où il est présenté un jeu épidémique en réseau dans lequel chaque joueur (région ou pays) cherche à trouver un compromis entre les pertes socio-économiques et sanitaires, tout en prenant en compte des contraintes telles que la disponibilité des unités de soins intensifs (USI). L'équilibre de Nash et l'équilibre de Nash généralisé sont analysés, et l'impact de la décentralisation sur l'efficacité est mesuré à l'aide de paramètres tels que le prix de l'anarchie (PoA) et le prix de la connectivité (PoC). Une application pratique du jeu à un scénario de Covid-19 est également illustrée. Le chapitre 3 étend l'analyse du chapitre 2 en incorporant la dynamique des opinions dans le contrôle décentralisé d'une épidémie en réseau. L'analyse se concentre sur l'existence et l'unicité de l'équilibre de Nash généralisé (GNE), et un algorithme pour atteindre le GNE est proposé. Les simulations identifient les scénarios où la décentralisation est acceptable en termes d'efficacité globale et soulignent l'importance de la dynamique des opinions dans les processus de prise de décision. Finalement, le chapitre 4 explore un modèle de duopole de Stackelberg dans le contexte des campagnes de marketing viral. L'objectif est de caractériser la stratégie d'allocation optimale des budgets publicitaires entre les régions pour maximiser la part de marché. Des stratégies d'équilibre sont déduites et des conditions pour un résultat de type "le gagnant rafle tout" sont établies. Les résultats théoriques sont complétés par des simulations numériques et un exemple illustrant la caractérisation de l'équilibre. Cette thèse offre des perspectives précieuses sur l'efficacité de la prise de décision décentralisée dans les dynamiques épidémiques et de marketing viral. Les résultats ont des implications pour la gestion des soins de santé, la concurrence commerciale et d'autres domaines connexes
This thesis investigates decentralized decision-making in epidemic and viral marketing dynamics. The mathematical framework of game theory is exploited to design and assess the effectiveness of decentralized strategies. The thesis begins with a review of mathematical tools, emphasizing graph theory and game theory. Chapter 2 presents a networked epidemic game where each player (region or country) seeks to implement a tradeoff between socio-economic and health looses, incorporating constraints such as intensive care unit (ICU) availability. Nash equilibrium and Generalized Nash equilibrium are analyzed, and the influence of decentralization on global efficiency is measured using metrics like the Price of Anarchy (PoA) and the Price of Connectedness (PoC). The practical application of the game to a Covid-19 scenario is illustrated. Chapter 3 extends the analysis of Chapter 2 by incorporating opinion dynamics into the decentralized control of a networked epidemic. A new game model is introduced, where players represent geographical aera balancing socio-economic and health losses; the game is built to implement features of practical interests and to possess some mathematical properties (e.g., posynomiality) which makes its analysis tractable. The analysis focuses on the existence and uniqueness of the Generalized Nash Equilibrium (GNE), and an algorithm for computing the GNE is proposed. Numerical simulations quantify the efficiency loss induced by decentralization in the presence and absence of opinion dynamics. The results identify scenarios where decentralization is acceptable in terms of global efficiency measures and highlight the importance of opinion dynamics in decision-making processes. Chapter 4 explores a Stackelberg duopoly model in the context of viral marketing campaigns. The objective is to characterize the optimal allocation strategy of advertising budgets across regions to maximize market share. A relatively simple Equilibrium strategies are derived, and conditions for a "winner takes all" outcome are established. Theoretical findings are complemented by numerical simulations and an example illustrating equilibrium characterization.This thesis offers valuable insights into the effectiveness of decentralized decision-making in the context of epidemic and viral marketing dynamics. The findings have implications for healthcare management, business competition, and related fields

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SIS (susceptible-infected-susceptible) and SIR (susceptible-infectedremoved) epidemiological models based on probabilistic cellular automaton (PCA) are used in order to simulate the temporal evolution of the number of people infected by dengue in the city of Rio de Janeiro in 2007, and to predict the cases of infection in 2008. In the PCA, three different sizes of lattices and two kinds of neighborhoods are utilized, and each time step of simulation is equivalent to one week of real time. A genetic algorithm (GA) is employed to identify the probabilities of the state transition S→I, in order to reproduce the historical series of 2007 related to this disease propagation. These probabilities depend on the number of infected neighbors. Time-varying and constant probabilities are taken into account. These models based on PCA and GA were able of satisfactorily fitting the data from 2007 and making a good prediction for 2008 (mainly about the total number of cases registered during 2008).
Usam-se modelos epidemiológicos SIS (suscetível-infectado-suscetível) e SIR (suscetível-infectado-removido) baseados em autômato celular probabilista (ACP) a fim de simular a evolução temporal do número de pessoas infectadas por dengue, na cidade do Rio de Janeiro em 2007, e de prever os casos de infecção em 2008. No ACP, utilizam-se reticulados de três tamanhos diferentes e dois tipos de vizinhanças, e cada passo de tempo da simulação equivale a uma semana de tempo real. Emprega-se um algoritmo genético (AG) para identificar os valores das probabilidades da transição de estados S→I, de modo a reproduzir a série histórica de 2007 relacionada à propagação dessa doença. Essas probabilidades dependem do número de vizinhos infectados. Probabilidades variantes e invariantes no tempo são consideradas. Esses modelos baseados em ACP e AG foram capazes de fazer um ajuste satisfatório dos dados de 2007 e de fornecerem uma boa previsão para 2008, (principalmente no que diz respeito ao número total de casos registrados em 2008).

Social networks play an important role in disseminating a piece of information in a population. Companies advertising a newly launched product, movie promotion, political campaigns, social awareness campaigns by governments, charity campaigns by NGOs and crowd funding campaigns by entrepreneurs are a few examples where an entity is interested in disseminating a piece of information in a target population, possibly under resource constraints. In this thesis we model information diffusion in a population using various epidemic models and study optimal campaigning strategies to maximize the reach of information. In the different problems considered in this thesis, information epidemics are modeled as the Susceptible-Infected, Susceptible-Infected-Susceptible, Susceptible-Infected-Recovered and Maki Thompson epidemic processes; however, we modify the models to incorporate the intervention made by the campaigner to enhance information propagation. Direct recruitment of individuals as spreaders and providing word-of-mouth incentives to the spreaders are considered as two intervention strategies (controls) to enhance the speed of information propagation. These controls can be implemented by placing advertisements in the mass media, announcing referral/cash back rewards for introducing friends to a product or service being advertised etc. In the different problems considered in this thesis, social contacts are modeled with varying levels of complexity---population is homogeneously mixed or follows heterogeneous mixing. The solutions to the problems which consider homogeneous mixing of individuals identify the most important periods in the campaign duration which should be allocated more resources to maximize the reach of the message, depending on the system parameters of the epidemic model (e.g., epidemics with high and low virulence). When a heterogeneous model is considered, apart from this, the solution identifies the important classes of individuals which should be allocated more resources depending upon the network considered (e.g. Erdos-Renyi, scale-free) and model parameters. These classes may be carved out based on various centrality measures in the network. If multiple strategies are available for campaigning, the solution also identifies the relative importance of the strategies depending on the network type. We study variants of the optimal campaigning problem where we optimize different objective functions. For some of the formulated problems, we discuss the existence and uniqueness of the solution. Sometimes our formulations call for novel techniques to prove the existence of a solution.

Social networks play an important role in disseminating a piece of information in a population. Companies advertising a newly launched product, movie promotion, political campaigns, social awareness campaigns by governments, charity campaigns by NGOs and crowd funding campaigns by entrepreneurs are a few examples where an entity is interested in disseminating a piece of information in a target population, possibly under resource constraints. In this thesis we model information diffusion in a population using various epidemic models and study optimal campaigning strategies to maximize the reach of information. In the different problems considered in this thesis, information epidemics are modeled as the Susceptible-Infected, Susceptible-Infected-Susceptible, Susceptible-Infected-Recovered and Maki Thompson epidemic processes; however, we modify the models to incorporate the intervention made by the campaigner to enhance information propagation. Direct recruitment of individuals as spreaders and providing word-of-mouth incentives to the spreaders are considered as two intervention strategies (controls) to enhance the speed of information propagation. These controls can be implemented by placing advertisements in the mass media, announcing referral/cash back rewards for introducing friends to a product or service being advertised etc. In the different problems considered in this thesis, social contacts are modeled with varying levels of complexity---population is homogeneously mixed or follows heterogeneous mixing. The solutions to the problems which consider homogeneous mixing of individuals identify the most important periods in the campaign duration which should be allocated more resources to maximize the reach of the message, depending on the system parameters of the epidemic model (e.g., epidemics with high and low virulence). When a heterogeneous model is considered, apart from this, the solution identifies the important classes of individuals which should be allocated more resources depending upon the network considered (e.g. Erdos-Renyi, scale-free) and model parameters. These classes may be carved out based on various centrality measures in the network. If multiple strategies are available for campaigning, the solution also identifies the relative importance of the strategies depending on the network type. We study variants of the optimal campaigning problem where we optimize different objective functions. For some of the formulated problems, we discuss the existence and uniqueness of the solution. Sometimes our formulations call for novel techniques to prove the existence of a solution.

Epidemic processes are relevant to studying the propagation of infectious diseases, but their current use extends also to the study of propagation of ideas in the society or memes and news in online social media. In most of the relevant applications epidemic spreading does not actually take place on a single network but propagates in a multilayer network where different types of interaction play different roles. This chapter provides a comprehensive view of the effect that multilayer network structures have on epidemic processes. The Susceptible–Infected–Susceptible (SIS) Model and the Susceptible–Infected–Removed (SIR) Model are characterized on multilayer networks. Additionally, it is shown that the multilayer networks framework can also allow us to study interacting Awareness and epidemic spreading, competing networks and epidemics in temporal networks.

A susceptible-infected-susceptible (SIS) model with a nonlinear infection rate, a forecast model based on autoregressive integrated moving average (ARIMA), and a forecast model based on long short-term memory (LSTM) artificial neural networks were developed using the COVID-19 epidemic data from four countries (China, Italy, the United Kingdom, Germany, France, and Poland) to simulate and forecast the epidemic trends in these countries. The models were compared in terms of forecast errors, and the LSTM model was found to forecast virus transmission very well.

The textbook mathematical model in epidemiology - SIS (Susceptible-Infected-Susceptible) provided the basis for proposing a new and improved model based on the observable behaviors of the current Covid-19 pandemic. The goal of this study was to analyze the behavior of the system and the influence of the LockDown factor on infected individuals. The model proposed here, called SIERDASHQ (Susceptible - Infected - Exposed - Recovered - Deceased - Asymptomatic - Symptomatic - Hospitalized - Quarantined), was simulated with values that expressed the situation of the pandemic at the national level, making it possible to compare data to the graphics produced by the program, which confirms the validity of the model.