Multi-Patch Epidemic Models with General Exposed and Infectious Periods

We study multi-patch epidemic models where individuals may migrate from one patch to another in either of the susceptible, exposed/latent, infectious and recovered states. assume that infections occur both locally with a rate depends on as well “from distance” all other patches. The migration processes among patches four states are assumed be Markovian, independent exposed periods. These periods have general distributions, not affected by possible migrations individuals. infection aspect introduces new formulation process, which, together processes, brings technical challenges proving functional limit theorems. Generalizing methods Pang Pardoux [ Ann. Appl. Probab. 32 (2022) 1615–1665], we establish law large number (FLLN) function central theorem (FCLT) for processes. In FLLN, is determined set Volterra integral equations. special case deterministic periods, becomes system ODEs delays. FCLT, given stochastic equations driven sum Brownian motions continuous Gaussian an explicit covariance structure.