Understanding dynamics of Plasmodium falciparum gametocytes production: Insights from an age-structured model

TL;DR

This study compares ODE and PDE models of malaria infection dynamics using patient data, revealing how parasite stage densities relate to infectiousness, aiding malaria control strategies.

Contribution

It introduces a PDE model tracking infected cell age and compares it with traditional ODE models, highlighting their similarities and differences in infection dynamics.

Findings

Both models fit data well with proper parameters.

ODE models overestimate early parasite densities with fewer compartments.

Gametocyte density correlates with host infectiousness.

Abstract

Many models of within-host malaria infection dynamics have been formulated since the pioneering work of Anderson et al. in 1989. Biologically, the goal of these models is to understand what governs the severity of infections, the patterns of infectiousness, and the variation thereof across individual hosts. Mathematically, these models are based on dynamical systems, with standard approaches ranging from K-compartments ordinary differential equations (ODEs) to delay differential equations (DDEs), to capture the relatively constant duration of replication and bursting once a parasite infects a host red blood cell. Using malariatherapy data, which offers fine-scale resolution on the dynamics of infection across a number of individual hosts, we compare the fit and robustness of one of these standard approaches (K-compartments ODE) with a partial differential equations (PDEs) model, which explicitly tracks the "age" of an infected cell. While both models perform quite similarly in terms of goodness-of-fit for suitably chosen K, the K-compartments ODE model particularly overestimates parasite densities early on in infections when the number of repeated compartments is not large enough. Finally, the K-compartments ODE model (for suitably chosen K) and the PDE model highlight a strong qualitative connection between the density of transmissible parasite stages (i.e., gametocytes) and the density of host-damaging (and asexually-replicating) parasite stages. This finding provides a simple tool for predicting which hosts are most infectious to mosquitoes -- vectors of \emph{Plasmodium} parasites -- which is a crucial component of global efforts to control and eliminate malaria.