Nonlocal Response in a Simple Epidemiological Model [chapter]

K. R. Heiderich, W. Huang, C. Castillo-Chavez
2002 IMA Volumes in Mathematics and its Applications  
We use a simple epidemiological model to investigate the e ects of a nonlocal feedback on the disease dynamics. We consider a context in which two groups can be identi ed: the population that is experiencing an epidemic and an \outside" population that acts primarily as a source and sink of uninfected individuals. The disease dynamics of the a icted group is e ected by immigration from the outside group, which, in turn, is e ected by the state of the disease. The response to this type of
more » ... this type of feedback can be investigated using a model in which the net in ux of susceptibles into the a icted population is a function of the disease prevalence in that group. We extend and generalize the analysis of Blythe et al. (1993a) to include more general net immigration functions. Since the population does not respond instantaneously to the state of the epidemic we include a time delay in the immigration function. We nd that the state-dependent recruitment, which was found to be destabilizing by Blythe et al., can actually stabilize the dynamics when such a time delay is included. Furthermore, consistent over(under)-estimation of the disease prevalence reduces(increases) the size of the endemic equilibrium populations.
doi:10.1007/978-1-4757-3667-0_8 fatcat:6hoishfwwfbohe6ccncmawdu2q