Temporal Evolution of Immunity Distributions in a Population with Waning and Boosting

Figure 1

Sketch of the mathematical models (3), (4), and (5). Susceptible hosts become infective after pathogen transmission. Infected hosts who recover enter the immune compartment which is structured by the level of immunity. Natural infection induces the maximal level of immunity . Immunity decays in time and when the immune status reaches the minimal value ; the recovered host becomes susceptible again. Meanwhile, exposure to the pathogen can boost the immune system and prolong protection.