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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 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 existence and stability of some semilinear problems

Mokhtar Kirane, Nasser-eddine Tatar (2000)

Archivum Mathematicum

We prove global existence and stability results for a semilinear parabolic equation, a semilinear functional equation and a semilinear integral equation using an inequality which may be viewed as a nonlinear singular version of the well known Gronwall and Bihari inequalities.

Global exponential stability of almost periodic solutions for a delayed single population model with hereditary effect

Qiyuan Zhou, Jianying Shao (2015)

Annales Polonici Mathematici

This paper is concerned with a delayed single population model with hereditary effect. Under appropriate conditions, we employ a novel argument to establish a criterion of the global exponential stability of positive almost periodic solutions of the model. Moreover, an example and its numerical simulation are given to illustrate the main result.

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