Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures

Abstract

In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number R0, is less than or equal to unity, then the disease-free equilibrium of the model is globally asymptotically stable. We also show that if the threshold value is greater than unity, then the model is uniformly persistent and has an endemic equilibrium. Moreover, using a Lyapunov functional technique, we obtain a sufficient condition under which the endemic equilibrium is globally asymptotically stable. The sufficient condition is satisfied if the transmission coefficients in the same groups are large or the per capita recovery rates are small.

Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents

“…First of all, it worth mentioning that general references to the spatial spread of infectious diseases include [5,22,38,41,52,60]. The basic assumption of our treatment, namely that all epidemiological compartments are distributed over the whole spatial domain, is opposed to the alternative metapopulation approach that describes spatial structure through the relations between a number of wellidentified sub-populations or "patches" (cf., e.g., [3,6,7,18,35,57,58]). In fact, the description of spatial structure by explicitly specifying the mobilities between "patches" is typical for characterizing the behavior of humans, who usually do not "disperse" in response to environmental stimuli (at least not in the relatively short time scales involved in epidemiological modelling) but undertake directed travels, while a description through a convection-diffusion-reaction mechanism is more suitable for non-human infectious agents such as spores, insects, and bacteria that would disperse.…”