Spatial transmission dynamics and numerical simulations of a monkeypox virus model with seasonality and environmental media

In this study, we establish a novel non-autonomous reaction–diffusion model, which couples the interactions among humans, rodents and the environment, and introduces seasonal variation and spatial heterogeneity to investigate the dynamic mechanism and persistence condition of monkeypox virus transmission. By using R0 as a threshold index, for the periodic system, we discuss the existence of periodic solutions and uniform persistence. In particular, for the constant coefficient case, by comparison theorem and fluctuation method, we tactfully prove that the disease will persist and the unique positive equilibrium state is globally asymptotically stable when R0c>1. Theoretical analysis and numerical results indicate that (1) environmental medium transmission and interpersonal transmission are the main ways that contribute to the overall risk of infection; (2) seasonal fluctuation and spatial heterogeneity both significantly enhance the intensity of transmission; (3) increasing the rate of recovery, hospitalization, and rodent isolation can effectively decline R0, thus reducing the scale of infection; (4) the system will tend toward the extinction of the disease, if the incubation period exceeds a certain critical threshold.