Dynamical Properties Of A New Sir Epidemic Model

Taking into account the depletion of food supply by all individuals, and the fact that chronic infectious diseases will not cause the infected individuals to lose their fertility completely, we first propose a new SIR epidemic model of ODE. For this model, we derive its basic reproduction number R₀, and show that the disease-free equilibrium point is globally asymptotically stable when R₀ ≤ 1, while the unique positive equilibrium point is globally asymptotically stable when R₀ > 1. Then we incorporate the spatial dispersion and free boundary condition into this ODE model. The well-posedness and longtime behaviors are obtained. Particularly, we find a spreading-vanishing dichotomy in which the basic reproduction number R₀ plays a crucial role.