Multi-patch deterministic and stochastic models for wildlife diseases

Abstract

Spatial heterogeneity and host demography have a direct impact on the persistence or extinction of a disease. Natural or human-made landscape features such as forests, rivers, roads, and crops are important to the persistence of wildlife diseases. Rabies, hantaviruses, and plague are just a few examples of wildlife diseases where spatial patterns of infection have been observed. We formulate multi-patch deterministic and stochastic epidemic models and use these models to investigate problems related to disease persistence and extinction. We show in some special cases that a unique diseasefree equilibrium exists. In these cases, a basic reproduction number R 0 can be computed and shown to be bounded below and above by the minimum and maximum patch reproduction numbers R j , j = 1, . . . , n. The basic reproduction number has a simple form when there is no movement or when all patches are identical or when the movement rate approaches infinity. Numerical examples of the deterministic and stochastic models illustrate the disease dynamics for different movement rates between three patches.

Modeling of Wildlife-Associated Zoonoses: Applications and Caveats

“…When the system includes wildlife hosts, species behavior or other ecological phenomena can be varied by region/patch (Gourley et al 2008) to incorporate spatial variations. Patch models have been used successfully in evaluating the dynamics of important zoonoses, such as rabies, hantaviruses, and plague, for which landscape features separate populations into discrete patches, and spatial variations in pathogen and/or host dynamics are observed (McCormack and Allen 2007).…”

Autômatos Celulares e Sistema Multiagente para Simulação da Propagação de Doenças

“…Porém, atualmente são realizados esforços no sentido de representar os contatos individuais, os efeitos do comportamento individual, a interação entre diferentes tipos de indivíduos e de comunidades, e os aspectos espaço-temporais de tais relações [1,22,23,18,24,13,7]. Algumas abordagens nesse sentido são discutidas a seguir.…”

Stochastic epidemic models revisited: analysis of some continuous performance measures

“…the papers by Coolen-Schrijner and van Doorn [11] and Artalejo et al [4]) and also to more complicated variants of the SIS and SIR epidemic models (see, e.g. some recent publications in this journal such as the papers by McCormack and Allen [24], Clémençon et al [9] and Martins et al [23]). …”