1. GLOBAL DYNAMICS OF A DISEASE MODEL INCLUDING LATENCY WITH DISTRIBUTED DELAYS.
- Author
-
Zhisheng Shuai and Van Den Driessche, P.
- Subjects
COMMUNICABLE diseases ,MATHEMATICAL models in medicine ,LYAPUNOV functions ,BIOMATHEMATICS ,MATHEMATICAL analysis ,MATHEMATICAL proofs - Abstract
An infectious disease model with two dis-tributed 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 TZo is defined and shown to give a sharp threshold. Specifically, if R
o < 1, then the disease-free equilibrium is globally asymptotically stable and the disease dies out; whereas if Ro > 1, then a Lyapunov func-tional 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. [ABSTRACT FROM AUTHOR]- Published
- 2011