Steady-state analysis of a continuum model for super-infection.
A large system of N strains of parasite and a single host is analyzed as a function of the degree of virulence in the strains when there is super-infection between hosts (more virulent strains can infect hosts that are already infected) and within-host transition between strains that is neutral. When this small amount of local switching is allowed, steady-state solutions converge to a continuous distribution as the number of strains increases. The resulting nonlinear-nonautonomous integro-differential equation is reduced to a fourth order boundary value problem (BVP) and the existence of positive solutions is proven. The methods here and associated BVP allow for a thorough exploration of parameter space for this class of models.
Ermentrout
Bard
B
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. bard@pitt.edu
Hastings
Stuart
S
D000818:Animals; D005075:Biological Evolution; D006790:Host-Parasite Interactions; D054884:Host-Pathogen Interactions; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D015163:Superinfection / Q000209:etiology*; D049490:Systems Biology; D014774:Virulence