Modelling The Impact of Misdiagnosis and Treatment on the Dynamics of Malaria Concurrent and Co-Infection with Pneumonia and Typhoid

Abstract

Mathematical models of malaria-pneumonia and malaria- typhoid concurrent and co-infection have been formulated to establish the effects of misdiagnosing pneumonia and typhoid as malaria. We performed stability analysis on the disease-free equilibrium (DFE) and the endemic equilibrium. The existence of locally asymptotic stability (LAS) of the DFE is investigated based on the reproduction number Ro. The DFE is shown to be locally asymptotically stable. if Ro < 1 and unstable if Ro > 1. The results show that the DFE is not globally asymptotically stable (GAS) even when Ro < 1. Instead, backward bifurcation occurs at Ro = 1. Backward bifurcation implies that having Ro < 1, although necessary, is not sufficient for curtailing endemicity of the disease. The general bifurcation theory and the center manifold theory were applied to determine the existence and stability of the endemic equilibrium near the threshold. A model for accurate diagnosis and prompt treatment of pneumonia is developed to compare the global stability of its disease-free and endemic equilibria with that of the case of misdiagnosis. Sensitivity analysis on both models show that the most sensitive parameter is the rate of misdiagnosis. For the malaria-typhoid model, the rate of becoming a carrier is also very sensitive. A major finding of this study is that misdiagnosis of pneumonia and typhoid leads to high endemicity of both diseases. Moreover, despite overuse of anti-malarials, misdiagnosis makes elimination of malaria not possible. Results of this study will help health care providers understand how misdiagnosis errors are made, reduce misdiagnosis and improve patient care.