Modelling the fear factor as delay spatiotemporal epidemic model

Ghilmana Sarmad

UAE University

"Modelling the fear factor as delay spatiotemporal epidemic model"

This paper studies a Susceptible-Protected-Infected-Recovered (SPIR) epidemic model incorporating both local and nonlocal diffusion to capture how fear of infection impacts population behaviour. We aim to establish the model’s well-posedness by proving the existence, uniqueness, and positivity of solutions. A key focus is deriving a variational expression for the basic reproduction number mathfrak{R_0}, which acts as a threshold indicator. When mathfrak{R_0} < 1, the disease-free equilibrium is globally stable, meaning the infection dies out. When mathfrak{R_0} > 1, the model predicts disease persistence and the existence of a stable endemic equilibrium, which we prove using Lyapunov functions. We consider two distinct scenarios: one where the diffusion of the susceptible population is absent, and another where the infected population does not diffuse. The model is also compared with the classical SIR model to evaluate the impact of protective measures aimed at reducing mathfrak{R_0} below unity for effective disease control.

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