Dynamics of a two-patch SIR model with disease surveillance mediated infection force

Travel between patches and behavior changes of susceptible individuals are two crucial factors affecting the disease dynamics for any emerging infectious disease. Therefore studies of their impacts on disease dynamics are of great importance, especially to public health policy -makers. In this paper, we propose an SIR model that incorporates these two factors into consideration. For our two -patch SIR model with infection force mediated by (past) disease surveillance, we identify the basic reproduction number and show how it is related to travel modified basic reproduction numbers. We also carry out stability and Hopf bifurcation analysis and obtain conditions under which the disease persists in one patch or both patches. Numerical simulations are carried out to illustrate how travel between two patches and disease surveillance mediated infection force affect the disease dynamics and thus provide us some helpful insights on proper control of emerging infectious diseases.