Mathematical Model and Analysis of Pneumonia on Children under five years with Malnutrition

Abstract

<title>Abstract</title> Pneumonia is an infection that affects one or both lungs and is caused by fungus, bacteria, or viruses while Malnutrition is defined as a dietary imbalance. Pneumonia and malnutrition are two different illnesses, however, they often coincide andcan have a substantial impact on child mortality in pneumonia-endemic regions.Considering their geographical proximity, there has been no mathematical analysisof their co-dynamics. To address this gap, we develop a deterministic pneumonia mathematical model that divides children into two groups: well-nourished andundernourished, to investigate the potential effect of malnutrition on pneumonia dynamics. The basic reproduction number of the proposed model is computed usingthe Next-Generation Matrix and both local and global stability of the disease-freeequilibrium is examined. Using the model parameters, the sensitivity analysis isperformed by using the Normalized forward sensitivity index to establish their effects on the basic reproduction number. Furthermore, Numerical simulations areprovided based on the model parameter values chosen. The results show that individuals who are malnourished have a higher chance of acquiring and dying frompneumonia than well-nourished individuals.