Analysis of Immune Response Mechanism of a Malaria-Autophagy & Immune Response Model
K. M. Koko *
Department of Mathematics and Statistics, Air Force Institute of Technology, Kaduna, Nigeria.
N. C. Umelo-Ibemere
Department of Statistics, Federal University of Technology, Owerri, Nigeria.
I. D. Ajana
Griggs Specialist Hospital, Lekki, Lagos, Nigeria.
I. C. Nwokike
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
W. I. Osuji
Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
S. Musa
Department of Mathematics, Sule Lamido University Kafin Hausa, Jigawa, Nigeria.
B. N. Anukam
Department of Chemistry, Federal University of Technology, Owerri, Nigeria.
O. C. Ezea
Department of Biology, Federal University of Technology, Owerri, Nigeria.
B. C. Ekeadinotu
Department of Mathematics, University of Agriculture and Environmental Sciences, Umuagwo–Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Malaria, caused by protozoan parasites of the genus Plasmodium and transmitted by infected female Anopheles mosquitoes, remains a major public health problem. In addition to adaptive immune responses, autophagy has been recognised as a cellular mechanism that may contribute to the removal of infected cells and pathogens. This study develops a nonlinear within-host mathematical model, formulated as a system of ordinary differential equations, to examine malaria infection in the presence of autophagy and immune response. The model describes interactions among healthy red blood cells, infected red blood cells, free malaria parasites, autophagic activity and activated immune effector cells. It incorporates autophagy-mediated and immune-mediated clearance of infected erythrocytes and free parasites. Positivity, boundedness and the existence of a positively invariant region are established to confirm the biological feasibility of the model. The basic reproduction number is derived using the next-generation matrix approach, and the stability properties of the disease-free equilibrium are analysed. The disease-free equilibrium is locally and globally asymptotically stable when the basic reproduction number is less than unity, indicating that infection cannot be sustained under this threshold condition. When the threshold exceeds unity, parasite persistence may occur depending on the model parameters and initial conditions. The analysis suggests that autophagy can complement immune-mediated clearance after infection has been initiated, although it does not appear explicitly in the initial invasion threshold.
Keywords: Malaria, autophagy, mathematical modeling, immune response, within-host dynamics, qualitative and stability analysis, basic reproduction number