Modeling the heterogeneous susceptibility and infectivity: A nonlocal state-structured SIR epidemic model

This work develops and analytically investigate a nonlocal state-structured SIR epidemic model governed by integro-differential equations, which characterizes heterogeneous host susceptibility and variable infectivity of infected individuals. Constructing appropriate Lyapunov functionals, we show that the basic reproduction number exclusively determines global stability of both disease-free and endemic steady states. Numerical simulations corroborate our theoretical findings and demonstrate the substantial impact of nonlocal kernels on disease transmission dynamics, besides, some significantly effective strategies are identified, including immunization of susceptible populations, contact-reduction measures, mitigation of pathogen-specific infectivity and retardation of disease progression. Furthermore, we apply an SVELITR model derived by discretizing the nonlocal state-structured model to project tuberculosis prevalence trends in China, providing quantitative insights into the efficacy of several interventions.