A MATHEMATICAL STUDY OF THE IMPLICIT ROLE OF INNATE AND ADAPTIVE IMMUNE RESPONSES ON WITHIN-HUMAN PLASMODIUM FALCIPARUM PARASITE LEVELS

Abstract

A within-human-host malaria parasite model, integrating key variables that influence parasite evolution-progression-advancement, under innate and adaptive immune responses, is analyzed. The implicit role of immunity on the steady state parasite loads and parasitemia reproduction number ([Formula: see text]), a threshold parameter measuring the parasite’s annexing ability of healthy red blood cells (HRBCs), eventually rendering a human infectious to mosquitoes, is investigated. The impact of the type of recruitment function used to model HRBC growth is also investigated. The model steady states and [Formula: see text], both obtained as functions of immune system variables, are analyzed at snapshots of immune sizes. Model results indicate that the more the immune cells, innate and adaptive, the more efficient they are at inhibiting parasite development and progression; consequently, the less severe the malaria disease in a patient. Our analysis also illustrates the existence of a Hopf bifurcation leading to a limit cycle, observable only for the nonlinear recruitment functions, at reasonably large [Formula: see text].