A SIRS epidemic model with infection-age dependence

Zhang, Zhonghua; Peng, Jigen

doi:10.1016/j.jmaa.2006.09.061

Cited by 22 publications

(6 citation statements)

References 18 publications

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“…While the general model from [13] was largely neglected until rather recently, most of the literature concentrating on the particular case of constant rates, there has been since the 1970s some papers considering age dependent epidemic models, see in particular [9]. More recently, several papers have introduced coupled PDE/ODE models for studying age of infection dependent both infectivity and recovery rate, see in particular [23,11,24,17,5] and chapter 13 in [18]. Since the beginning of the Covid-19 pandemic, a huge number of papers have been produced, with various models of the propagation of this disease.…”

Section: Introductionmentioning

confidence: 99%

Functional law of large numbers and PDEs for epidemic models with infection-age dependent infectivity

Pang¹,

Pardoux²

2021

Preprint

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We study epidemic models where the infectivity of each individual is a random function of the infection age (the elapsed time of infection). To describe the epidemic evolution dynamics, we use a stochastic process that tracks the number of individuals at each time that have been infected for less than or equal to a certain amount of time, together with the aggregate infectivity process. We establish the functional law of large numbers (FLLN) for the stochastic processes that describe the epidemic dynamics. The limits are described by a set of deterministic integral equations, which has a further characterization using PDEs under some regularity conditions. The solutions are characterized with boundary conditions that are given by a system of Volterra equations. We also characterize the equilibrium points for the PDEs in the SIS model with infection-age dependent infectivity. To establish the FLLNs, we employ a useful criterion for weak convergence for the two-parameter processes together with useful representations for the relevant processes via Poisson random measures.

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Section: Introductionmentioning

confidence: 99%

Functional law of large numbers and PDEs for epidemic models with infection-age dependent infectivity

Pang¹,

Pardoux²

2021

Preprint

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“…Many mathematical models on this topic have been studied [12][13][14][15][16][17]. Reference [17] states that, in infinite scale-free networks, epidemic processes do not possess an epidemic threshold below which diseases cannot produce a major epidemic outbreak or the inset of an endemic state.…”

Section: Introductionmentioning

confidence: 99%

The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network

Lou

Ruggeri

2010

Journal of Mathematical Analysis and Applications

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We examine epidemic threshold and dynamics for sexually transmitted diseases (STDs) spread using a multiple susceptible-infected-removed-susceptible ODE model on scalefree networks. We derive the threshold for the epidemic to be zero in infinite scalefree network. For a hard cut off scale-free network, we also prove the stability of disease-free equilibrium and the persistence of STDs infection. The effects of two immunization schemes, including proportional scheme and targeted vaccination, are studied and compared. We find that targeted strategy compare favorably to a proportional scheme in terms of effectiveness. Theory and simulations both prove that an appropriate condom using has prominent effect to control STDs spread on scale-free networks.

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“…Over the last three decades, the infection-agedependent epidemic models have been studied extensively and a number of mathematical models have been proposed to address different aspects related to age in epidemic transmission. Mathematical issues such as existence of steady state solutions as well as stability property have been analysis [14][15][16][17][18][19][20]. An excellent review regarding the epidemic modelling and age-structured epidemic modelling can be found in [21].…”

Section: Introductionmentioning

confidence: 99%

Steady State Solution and Stability of an Age-Structured MSIQR Epidemic Model

Qiao

Tian

2010

IIM

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The importance of epidemiology in our life has stimulated researchers to extend the classic Susceptibles-Infectives-Removed (SIR) model to sophisticated models by including more factors in order to give detailed transmission dynamics of epidemic diseases. However, the integration of the quarantine policy and age-structure is less addressed. In this work we propose an age-structured MSIQR (temporarily immune-susceptibles-infectives-quarantined-removed) model to study the 0 1   impact of quarantine policies on the spread of epidemic diseases. Specifically, we investigate the existence of steady state solutions and stability property of the proposed model. The derived explicit expression of the basic reproductive number shows that the disease-free equilibrium is globally asymptotically stable if, and that the unique endemic equilibrium exists if. In addition, the stability conditions of the endemic equilibrium are derived.

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A SIRS epidemic model with infection-age dependence

Cited by 22 publications

References 18 publications

Functional law of large numbers and PDEs for epidemic models with infection-age dependent infectivity

Functional law of large numbers and PDEs for epidemic models with infection-age dependent infectivity

The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network

Steady State Solution and Stability of an Age-Structured MSIQR Epidemic Model

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