A strategy for constructing tractable epidemic models of malarial superinfection.

Abstract

Superinfection, that is the concurrent presentation of separately-acquired infections, is an important feature of several infectious diseases. A particularly pertinent example is malaria. Population-level compartment models allowing for malarial superinfection may take the form of countably infinite systems of ordinary differential equations (ODEs), which poses complications for simulation and analysis.

Here, we present a novel strategy for deriving tractable systems of integrodifferential equations (IDEs) for epidemic models of malarial superinfection. Our approach is predicated on the fact that we can characterise within-host dynamics using a network of infinite-server queues with a time dependent batch arrival rate that is a function of the intensity of mosquito-to-human transmission

We shall illustrate this approach in the context of a classical model of superinfection for Plasmodium falciparum malaria. By observing that this classical deterministic compartment model — comprising a countably infinite system of ODEs — has the same form as the Kolmogorov forward differential equations for an infinite server queue, we recover a reduced system of integro-differential equations (IDEs). The resultant systems of IDEs are amenable to numerical solution, allowing us to explore the transient, population-level dynamics of superinfection without resorting to approximation. We can also derive threshold parameters governing the existence of non-trivial (endemic) equilibria.

This approach can be generalised to account for additional biological complexity, in particular the accrual of the hypnozoite reservoir — a bank of dormant liver-stage parasites that can activate repeated relapses of Plasmodium vivax malaria. It can also be used in models that take into account demography, drug treatment and the development of immunity.

This is joint work with Somya Mehra and James McCaw