Abstract
This contribution develops a delayed diffusive SEIVS epidemic model for predicting and quantifying transmission dynamics for some slowly progressive diseases with long-term latent stage, governed by reaction–diffusion integro-differential equations taking distributed delays of latency and waning immunity, spatial mobility, vaccination strategies, temporary immunity into account. Necessary and sufficient conditions not only for global asymptotic stability of the disease-free and endemic equilibria are just determined by the basic reproduction number, but also for the existence and nonexistence of traveling wave solution connecting the two equilibria fully depend on the minimal wave velocity and the basic reproduction number. The targeted model with exponential distributions is applied to fit the pulmonary tuberculosis (TB) case data in China, predict its spread trend and provide us with an improving understanding of the effectiveness of a few interventions. Furthermore, our analytical findings are numerically corroborated to characterize the spatiotemporal evolution of pulmonary TB.
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