GLOBAL DYNAMICS OF A REACTION-DIFFUSION SEIVQR EPIDEMIC MODEL IN ALMOST PERIODIC ENVIRONMENTS

We have formulated an almost periodic reaction-diffusion SEIVQR epidemic model that incorporates quarantine, vaccination, and a latent period. In contrast to prior methods that analyze stability by using Lyapunov functions, we establish the global threshold dynamics of this model by using the upper Lyapunov exponent $\lambda^*$. Our results demonstrate that the disease-free almost periodic equilibrium is globally asymptotically stable if $\lambda^*<0$, whereas the disease uniformly persists if $\lambda^*>0$. To further validate our conclusions, we conducted numerical simulations of the model.