Dynamical properties of a new SIR epidemic model

Taking into account the depletion of food supply by all individuals, and fact that chronic infectious diseases will not cause infected individuals to lose their fertility completely, we first propose a new SIR epidemic model ODE. For this model, derive its basic reproduction number $ \mathcal{R}_0 $, show disease-free equilibrium point is globally asymptotically stable when \mathcal{R}_0\le1 while unique positive \mathcal{R}_0>1 $. Then incorporate spatial dispersion free boundary condition ODE model. The well-posedness longtime behaviors are obtained. Particularly, find spreading-vanishing dichotomy in which plays crucial role.