Figure 3.
Bistability with acute and chronic infections. Within-host biomass dynamics as a function of parasite attack rate (resource uptake rate). Low attack rate values (0 < σC < 0.5) exclusively allow for acute infections (no equilibrium with positive parasite biomass, a,c left of PT). High attack rate values (σC > 0.89) exclusively allow for chronic infections (only an equilibrium with high parasite biomass, b,c, right of IT). Intermediate attack rate values result in bistability between acute and chronic infection states, meaning that both the state with extinct parasite (acute) and high parasite biomass (chronic) are stable equilibria. The relationship between time series (a,b) and equilibrium solutions (c–f) is shown. Time series (a,b) illustrate the induction and waning of immune response in an acute infection (a) and the elevated endpoint in a chronic infection (b). Grey shaded area: bistable region, enclosed between the persistence threshold (PT) and invasion threshold (IT) (see electronic supplementary material). Bold, grey arrows (c) indicate dynamics in time as approaching equilibria. F = 1.5, εAmin = 0.4 (compare with electronic supplementary material, figure S7); other parameters have default values. (Online version in colour.)