Theory of possible effects of the Allee phenomenon on the population of an epidemic reservoir.
We investigate possible effects of high-order nonlinearities on the shapes of infection refugia of the reservoir of an infectious disease. We replace Fisher-type equations that have been recently used to describe, among others, the Hantavirus spread in mouse populations by generalizations capable of describing Allee effects that are a consequence of the high-order nonlinearities. After analyzing the equations to calculate steady-state solutions, we study the stability of those solutions and compare to the earlier Fisher-type case. Finally, we consider the spatial modulation of the environment and find that unexpected results appear, including a bifurcation that has not been studied before.
Kumar
Niraj
N
Department of Physics and Astronomy and Consortium of the Americas for Interdisciplinary Science, University of New Mexico, Albuquerque, New Mexico 87131, USA.
Kuperman
M N
MN
Kenkre
V M
VM
D000465:Algorithms; D000818:Animals; D004196:Disease Outbreaks; D004197:Disease Reservoirs; D004777:Environment; D006476:Orthohantavirus / Q000472:pathogenicity; D018778:Hantavirus Infections / Q000453:epidemiology / Q000635:transmission; D016014:Linear Models; D016015:Logistic Models; D051379:Mice; D008954:Models, Biological; D017711:Nonlinear Dynamics