Spread of infectious diseases in a hyperbolic reaction-diffusion susceptible-infected-removed model

Abstract

A one-dimensional hyperbolic reaction-diffusion model of epidemics is developed to describe the dynamics of diseases spread occurring in an environment where three kinds of individuals mutually interact: the susceptibles, the infectives, and the removed. It is assumed that the disease is transmitted from the infected population to the susceptible one according to a nonlinear convex incidence rate. The model, based upon the framework of extended thermodynamics, removes the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models. Linear stability analyses are performed to study the nature of the equilibrium states against uniform and nonuniform perturbations. Emphasis is given to the occurrence of Hopf and Turing bifurcations, which break the temporal and the spatial symmetry of the system, respectively. The existence of traveling wave solutions connecting two steady states is also discussed. The governing equations are also integrated numerically to validate the analytical results and to characterize the spatiotemporal evolution of diseases.

Is an Entropy-Based Approach Suitable for an Understanding of the Metabolic Pathways of Fermentation and Respiration?

“…As a result, there is an increase of the possible number of responses of the system to environment changes or equivalently the concept of Darwinian fitness [43,44].…”

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

“…For example, spatial patterns are indicative of the large scale trends of epidemics or of the rates of spread through space, which in turn may guide policy decisions. The types of patterns found in epidemiological studies include stationary patterns [38][39][40][41][42], wave patterns [43][44][45][46][47], patch invasion [48], and others [49][50][51][52].…”

Wave features of a hyperbolic model for the within-season dynamics of insect pathogens

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