COS 282-1 - Parasite diversity induces a critical transition between low and high prevalence in a structured population model of malaria transmission

Abstract: A hyper-diverse class of pathogens of humans and wildlife, including the malaria parasite Plasmodium falciparum, rely on multigene families to encode antigenic variation. As a result, high (asymptomatic) prevalence is observed despite high immunity in local populations under high-transmission settings. The vast diversity of “strains” and genes encoding this variation challenges the application of established models for the population dynamics of such infectious diseases. Agent-based models have been formulated to address theory on strain coexistence and structure, but their complexity limits application to gain insights on population dynamics. Here, we develop an alternative formulation in the form of a structured SI (Susceptible-Infected) population model in continuous time, where individuals are classified by both age and the diversity of parasites they have been exposed to and retain in their specific immune memory. We analyze the population dynamics and bifurcation structure of this system of partial-differential equations as a function of transmission intensity. We show the existence of alternative steady-states and a critical transition in the model as we vary transmission intensity. Malaria prevalence exhibits a tipping point with transmission intensity. Although alternative equilibria disappear when immigration of parasite diversity becomes sufficiently large, the system retains the sharp transition from low to high prevalence with increasing transmission. We describe concomitant changes in parasite genetic diversity and force of infection, to explain the critical transition as the result of a positive feedback between these two variables. Results emphasize the importance of explicitly considering pathogen diversity and associated specific immune memory in the population dynamics of hyper-diverse epidemiological systems. This statement is discussed in a more general context for ecological competition systems with hyper-diverse trait spaces.