This article is cited in 6 papers

Epidemic dynamics in a heterogeneous incompletely isolated population with allowance for seasonal variations in the infection rate

A. N. Gerasimov^a, V. N. Razzhevaikin<sup>b

a</sup> Moscow Medical Academy, ul. Trubetskaya 8, str. 2, Moscow, 119991, Russia
^b Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: Mathematical parasite-host models are generalized to the case when the population members differ in susceptibility and contagiousness, there is an external source of infection, and the model parameters depend periodically (seasonally) on time. The model is proved to have a periodic solution that is unique and exponentially stable for sufficiently small periodic oscillations of the coefficients.

Key words: parasite-host system of differential equations, solution existence and uniqueness, exponential stability of the solution.

UDC: 519.677

Received: 22.05.2007

 English version: Computational Mathematics and Mathematical Physics, 2008, 48:8, 1406–1417

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