Steady-state analysis of a continuum model for super-infection
Bard Ermentrout1, Stuart Hastings
1Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. bard@pitt.edu
Abstract:
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.
Related Concept Videos
Modeling with Differential Equations
One-Compartment Model: IV Infusion
The one-compartment model for IV infusion uses mathematical equations to describe the rate of change in drug quantity in the body. At steady-state or infusion equilibrium, the drug input...
Compartment Models: Single-Compartment Model
Steady State Concentration
Most drugs are administered in repeated doses at fixed intervals or through continuous intravenous...
Pharmacodynamic Models: Linear Concentration–Effect Model
Two-Compartment Open Model: IV Infusion
The model illustrates the decrease in plasma drug concentration from the central compartment with a specific equation. It shows that under steady-state conditions, the drug's input rate...

