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An improved Susceptible-Infected-Susceptible (SIS) epidemic diffusion model with population migration between two cities is modeled. Global stability conditions for both the disease-free equilibrium and the endemic equilibrium are analyzed and proved. The main contribution of this paper is reflected in epidemic modeling and analysis which considers unequal migration rates, and only susceptible individuals can migrate between the two cities. Numerical simulation shows when the epidemic diffusion system is stable, number of infected individuals in one city can reach zero, while the number of infected individuals in the other city is still positive. On the other hand, decreasing population migration in only one city seems not as effective as improving the recovery rate for controlling the epidemic diffusion. [ABSTRACT FROM AUTHOR]

Abstract: Moneim and Greenhalgh [I.A. Moneim, D. Greenhalgh, Use of a periodic vaccination strategy to control the spread of epidemics with seasonally varying contact rate, Math. Biosci. Eng. 2 (2005) 591–611] proposed an SEIRS epidemic model with general periodic vaccination strategy and seasonally varying contact rate. Their investigation shows that when , there exists a globally asymptotically stable disease-free periodic state, and when , the disease-free solution is unstable and there is at least one positive periodic solution. But they did not find the threshold condition for uniform persistence and extinction of the disease, and left a conjecture—that is, whether the basic reproduction ratio of the time-averaged system can be the threshold parameter or not. The present paper gives a negative answer to this question and provides a thorough global dynamics for this system. Numerical simulations which show our theoretical results are also given. [Copyright &y& Elsevier]