Mathematical analysis of the impact of transmission-blocking drugs on the population dynamics of malaria

Abstract

Recently, promising clinical advances have been made in the development of antimalarial drugs that block the parasite transmission and also cures the disease and has prophylactic effects, called transmission-blocking drugs (TBDs). The aim of this paper is to develop and analyze a population level compartmental model of human-mosquito interactions that takes into account an intervention using TBDs. We do this by extending the SEIRS-SEI type model to include a class of humans who are undergoing the treatment with TBDs and a class of those who are protected because of successful treatment. Before we proceed with an analysis of the model’s stability and bifurcation behaviours, we start by ensuring that the model is well-posed in a biologically feasible domain. Mathematical analysis indicates that the model exhibits a forward and backward bifurcation under certain conditions. Results from our analysis shows that the effect of treatment rate on reducing reproduction number depends on other key parameters such as the efficacy of the drug. The projections of the validated model show the benefits of using TBDs in malaria control in preventing new cases and reducing mortality. In particular, we find that treating 35% of the population of Sub-Saharan Africa with a 95% efficacious TBD from 2021 will result in approximately 82% reduction on the number of malaria deaths by 2035.