MODELLING THE INTERACTIONS OF SICKLE CELL GENE ON MALARIA TRANSMISSION DYNAMICS
Vol. 9(2) July 2021, No. 19, pp. 222-240
R. I. GWERYINA, O. ABAH AND F. S. KADUNA
This article proposes a deterministic three-dimensional system for the transmission dynamics of malaria in a mosquito and genetically stratified human populations. To assess the impact of intervention measures, we derive a formula for the basic reproduction number, Ri of infection and examine the existence of infection endemic equilibria. The model is found to exhibit backward bifurcation (where the infection-free and infection endemic equilibria co-exist), with this situation, the usual epidemiological condition of malaria elimination among each genotype population, Ri < 1 , is no longer sufficient, even though necessary. The model is also shown to undergo a Hopf bifurcation under certain conditions. Further, the infection-free equilibrium is shown to stable globally in the instance Ri < 1 and on the condition that there are no persisting mosquito bites in the population. The global stability of infection endemic equilibrium is also studied when the basic reproduction number is greater than unity. Finally, we provide numerical simulations to illustrate our analytical findings with brief discussion.