Recurrent malaria dynamics: insight from mathematical modelling

In this study, a new mathematical model for malaria dynamics featuring all the three categories of recurrent malaria—recrudescence, relapse and re-infection—is presented and rigorously analysed. The formulated model is a nine-dimensional system of ordinary differential equations describing the population dynamics of humans and mosquitoes interaction. The analysis carried out reveals that the model exhibits a backward bifurcation phenomenon in the presence of re-infection, which is the recurrence of malaria symptoms due to infection from new parasites, whenever the associated basic reproduction number is less than unity. However, further investigation shows that the occurrence of backward bifurcation can be successfully ruled out in the absence of re-infection. The global dynamics of the malaria model is established via Lyapunov functions method and the asymptotic behaviour of the system is quantitatively illustrated.