Bifurcation and Sensitivity Analysis of Malaria–Schistosomiasis Co-infection Model

Malaria–schistosomiasis co-infection have major impacts on the host immune response and co-infection is extensive. Mathematical models of malaria–schistosomiasis co-infection are not common in literature. A mathematical model to describe the co-interaction between malaria and schistosomiasis was formulated as a system of nonlinear ordinary differential equations. Qualitative and comprehensive mathematical techniques were applied to analyse the model. The basic reproduction number was computed using the next generation matrix method, while the centre manifold theory was used to show that the malaria–schistosomiasis endemic equilibrium is locally asymptotically stable when the associated reproduction numbers are greater than unity. Sensitivity analysis was further carried out to investigate the impact of the model parameters on the transmission and spread of the diseases. As a parameter of the co-infection model was varied, the stability of the equilibrium point changed and this suggested the possibility of a forward bifurcation at R M S = 1. This has a great implication for public health and control measures. Numerical simulations were performed to verify our theoretical findings. © 2017, Springer (India) Private Ltd.