The consequences of habitat fragmentation on disease propagation

Abstract

In this paper, we present and analyse a simple model for disease transmission in a population that can freely move among two different geographical locations. In contrast to some recent contributions in the literature that focus on the epidemiological aspects of disease eradication [L.J.S. Allen, B.M. Bolker, Y. Lou, and A.L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic patch model, SIAM J. Appl. Math. 67 (2007), pp. 1283–1309; D. Gao and S. Ruan, An SIS patch model with variable transmission rate, Math. Biosci. 232 (2011), pp. 110–115; Y. Jin and W. Wang, The effect of population dispersal on the spread of a disease, J. Math. Anal. Appl. 308 (2005), pp. 343–364] through the assessment of the basic reproductive number and its implications in fragmented environments, the purpose of this investigation is rather to establish the effects of habitat disruption on the disease evolution and spread. In fact, our analysis discusses environment modifications leading either to a different topology, that is, unidirectional migrations only, or to changes in individual habits, for instance diseased animals unable to undertake the migration effort, as possible tools for disease eradication. Transcritical bifurcations are identified, leading at times to an ecosystem with endemic disease.