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Generalization of the Kermack-McKendrick SIR Model to a Patchy Environment for a Disease with Latency

J. Li, X. Zou (2009)

Mathematical Modelling of Natural Phenomena

In this paper, with the assumptions that an infectious disease has a fixed latent period in a population and the latent individuals of the population may disperse, we reformulate an SIR model for the population living in two patches (cities, towns, or countries etc.), which is a generalization of the classic Kermack-McKendrick SIR model. The model is given by a system of delay differential equations with a fixed delay accounting for the latency and non-local terms caused by the mobility of the...

Global Asymptotic Stability of Equilibria in Models for Virus Dynamics

J. Prüss, R. Zacher, R. Schnaubelt (2008)

Mathematical Modelling of Natural Phenomena

In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R0 of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the virus-free equilibrium has this property, and in case R0 > 1 there is a unique disease equilibrium which takes over this...

Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections

Yukihiko Nakata, Gergely Röst (2015)

Mathematica Bohemica

We describe the global dynamics of a disease transmission model between two regions which are connected via bidirectional or unidirectional transportation, where infection occurs during the travel as well as within the regions. We define the regional reproduction numbers and the basic reproduction number by constructing a next generation matrix. If the two regions are connected via bidirectional transportation, the basic reproduction number R 0 characterizes the existence of equilibria as well as...

Global exponential stability of positive periodic solutions for an epidemic model with saturated treatment

Bingwen Liu (2016)

Annales Polonici Mathematici

This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.

Global stability analysis and control of leptospirosis

Kazeem Oare Okosun, M. Mukamuri, Daniel Oluwole Makinde (2016)

Open Mathematics

The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction...

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