title: Modelling diseases with relapse and nonlinear incidence of infection: a multi-group epidemic model.
abstract: In this paper, we introduce a basic reproduction number for a multi-group SIR model with general relapse distribution and nonlinear incidence rate. We find that basic reproduction number plays the role of a key threshold in establishing the global dynamics of the model. By means of appropriate Lyapunov functionals, a subtle grouping technique in estimating the derivatives of Lyapunov functionals guided by graph-theoretical approach and LaSalle invariance principle, it is proven that if it is less than or equal to one, the disease-free equilibrium is globally stable and the disease dies out; whereas if it is larger than one, some sufficient condition is obtained in ensuring that there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. Furthermore, our results suggest that general relapse distribution are not the reason of sustained oscillations. Biologically, our model might be realistic for sexually transmitted diseases, such as Herpes, Condyloma acuminatum, etc.
authors: a School of Mathematics and Statistics , Southwest University , Chongqing 400715 , People's Republic of China.
authors: Jinliang
authors: J
authors: Wang
authors: Jingmei
authors: J
authors: Pang
authors: Xianning
authors: X
authors: Liu
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D019353:Endemic Diseases; D058872:Epidemics; D006801:Humans; D015994:Incidence; D008954:Models, Biological; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D012008:Recurrence
keywords: 34D30; 92D30; Lyapunov functional; global stability; multi-group epidemic model; relapse distribution