AN SIR EPIDEMIC MODEL WITH NONLINEAR BIRTH PULSES

摘要: An SIR epidemic model with logistic population dynamics and nonlinear birth pulses is considered in this paper. The basic reproductive number R0 deflned. We obtain the exact infection-free periodic solution of impulsive system. By using discrete dynamical system generated by a monotone, concave map for population, we prove that globally asymptotically stable if 1. Numerical simulation given Keywords. Dynamics; Epidemic model; Basic number; Globally stable; solution; positive solution. AMS (MOS) subject classiflcation: 92B05, 34A37, 34D23, 34K18. 1 Introduction formulation Impulsive difierential equations have been widely used to study dynamic behavior ecological systems models. Compared tradi- tional ordinary equations, provide natural description such systems. They generally describe phenom- ena which steep or instantaneous changes can be found almost every branch applied sciences. For example, flsherman may go flshing at same time once day week; vaccination children aged one several years two years; births some wild animals seasonal occur regular so on. In terms mathematical treatment, presence impulses gives mixed nature, both continuous discrete. qualitative properties are embodied those sys- tem determines state after pulse previous pulse. theory references (1,2). often deeply perturbed efiect has received much attention from researchers. reference (3), researchers studied existence time-dependent predator-prey efiects. (4), authors global behaviors