Abstract
The COVID-19 pandemic has refocused research on mathematical modeling and analysis of epidemic dynamics. We analytically investigate a partial differential equation (PDE) based, compartmental model of spatiotemporal epidemic spread, marked by strongly nonlinear infection forces representing the infection transmission mechanism. Employing higher-order perturbation analysis and computing the local Lyapunov exponent, we observe the emergence of dynamic instabilities induced by stochastic environmental forces driving the epidemic spread. Notably, the instabilities are uncovered using third-order perturbations whilst they are not observed under second-order perturbations. Moreover, the onset of instability is more likely with increasing noise strength of the stochastic environmental forces.
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