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Volume 19,     Number 3,     Fall 2011

 

GLOBAL DYNAMICS OF A DISEASE MODEL
INCLUDING LATENCY WITH DISTRIBUTED
DELAYS
ZHISHENG SHUAI AND P. VAN DEN DRIESSCHE

Abstract. An infectious disease model with two distributed delays is proposed to incorporate both the latency of the infection in a vector and the latent period in an infected host. The basic reproduction number R0 is defined and shown to give a sharp threshold. Specifically, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable and the disease dies out; whereas if R0 > 1, then a Lyapunov functional is used to prove that the endemic equilibrium is globally asymptotically stable, thus the disease persists at an endemic level. This model includes and extends several delay models in the literature.

 

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