Malaria and malnutrition in children: A mathematical model

Abstract

Malaria, a vector-borne disease, and malnutrition, an imbalance of essential nutrients, or poor nutrition are two major causes of childhood mortality in malaria endemic regions. Despite their geographical overlap, mathematical investigation of their co-dynamics is lacking. To fill this gap, we formulate a deterministic model of malaria subdividing the children population into two groups; those who are well-nourished and the poorly nourished, in order to investigate the potential effect of malnutrition on malaria dynamics. The proposed model is analyzed, the basic reproduction number is computed, and the local asymptotic stability of the disease-free equilibrium is proven. By applying the Centre Manifold Theory, the endemic equilibrium exists and may not be globally asymptotically stable owing to the system exhibiting the phenomenon of backward bifurcation under certain conditions. Using the chosen model parameter values, numerical simulations are provided. The endemic equilibrium is globally asymptotically stable and this persistence of the disease implies much efforts should be done to mitigate the spread of malaria and malnutrition in the population. With no competitive exclusion, the modification parameter which accounts for the relative infectiousness of children poorly nourished to malaria infection is used to investigate the potential impact of malnutrition on the dynamics of malaria. Our results reveal that to mitigate the spread of malaria in young children, a balanced diet is imperative to reduce morbidity and mortality.

Keywords

• Malaria
• Malnutrition
• Dynamical systems
• Reproduction number
• Bifurcation