Abstract
Human malaria remains a major killer disease worldwide, with nearly half (3.2 billion) of the world’s population at risk of malaria infection. The infectious protozoan disease is endemic in tropical and subtropical regions, with an estimated 212 million new cases and 429,000 malaria-related deaths in 2015. An in-host mathematical model ofPlasmodium falciparummalaria that describes the dynamics and interactions of malaria parasites with the host’s liver cells (hepatocytic stage), the red blood cells (erythrocytic stage), and macrophages is reformulated. By a theoretical analysis, an in-host basic reproduction numberR0is derived. The disease-free equilibrium is shown to be locally and globally asymptotically stable. Sensitivity analysis reveals that the erythrocyte invasion rateβr, the average number of merozoites released per bursting infected erythrocyteK, and the proportion of merozoites that cause secondary invasions at the blood phaseζare the most influential parameters in determining the malaria infection outcomes. Numerical results show that macrophages have a considerable impact in clearing infected red blood cells through phagocytosis. Moreover, the density of infected erythrocytes and hence the severity of malaria are shown to increase with increasing density of merozoites in the blood. Concurrent use of antimalarial drugs and a potential erythrocyte invasion-avoidance vaccine would minimize the density of infected erythrocytes and hence malaria disease severity.
Highlights
Human malaria remains a major killer disease worldwide, with nearly half (3.2 billion) of the world’s population at risk of malaria infection [1]
The simulations are performed to illustrate the possible dynamics of the red blood cells, the malaria parasite, and macrophages
A keen look at Figure 7(b) reveals that the infected red blood cells begin to appear after about 10–15 days of initial infection. This is consistent with the incubation period of Plasmodium falciparum malaria [49]
Summary
Human malaria remains a major killer disease worldwide, with nearly half (3.2 billion) of the world’s population at risk of malaria infection [1]. Hepatocyte invasion is accompanied by the formation of parasitophorous vacuole (PV) around the sporozoite [7] They form preerythrocytic schizonts and multiply by schizogony, culminating in the production of 8–24 first generation merozoites that are released into the International Journal of Mathematics and Mathematical Sciences blood when the liver schizonts burst open [8]. The rest of the daughter merozoites develop into sexual forms called gametocytes [10] These gametocytes are later taken up by other female Anopheles mosquitoes during feeding [13]. Adaptive immune system further provides protection against future exposures to malaria pathogens Innate immune cells such as the Plasmodium falciparum DNA, natural killer cells (NK cells), dendritic cells (DCs), macrophages, natural killer T (NKT) cells, and T cells are involved in the clearance of circulating parasites, infected erythrocytes, and infected hepatocytes [14].
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