On the dynamics of an epidemic patch model with mass-action transmission mechanism and asymmetric dispersal patterns.

This paper examines an epidemic patch model with mass-action transmission mechanism and asymmetric connectivity matrix. Results on the global dynamics of solutions and the spatial structures of endemic equilibrium (EE) solutions are obtained. In particular, we show that when the basic reproduction number R0 is less than one and the dispersal rate of the susceptible population ds is large, the population would eventually stabilize at the disease-free equilibrium. However, the disease may persist if ds is small, even if R0 < 1. In such a scenario, explicit conditions on the model parameters that lead to the existence of multiple EE are identified. These results provide new insights into the dynamics of infectious diseases in multipatch environments. Moreover, results in Li and Peng (Stud Appl Math. 2023;150(3):650-704), which is for the same model but with symmetric connectivitymatrix, are generalized and improved. [ABSTRACT FROM AUTHOR]