Mathematical Model for Hepatocytic-Erythrocytic Dynamics of Malaria

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 of Plasmodium falciparum malaria 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 number 0 is derived. The disease-free equilibrium is shown to be locally and globally asymptotically stable. Sensitivity analysis reveals that the erythrocyte invasion rate , the average number of merozoites released per bursting infected erythrocyte , and the proportion of merozoites that cause secondary invasions at the blood phase are 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.

The transmission mechanism theory of disease dynamics: Its aims, assumptions and limitations

“…The global exchange of pathogen between organs or microcommunities or microenvironments is usually through the circulatory system or through the lymphatic system. For typical examples of single scale models developed at this scale organization see ( Orwa, Mbogo, & Luboobi, 2018 ; Selemani, Luboobi, & Nkansah-Gyekye, 2017 ) for malaria infections and ( Barker & Vaidya, 2020 ; Chen, Cheng, & Rong, 2019 ) for viral infections in the context of environmental transmission. Therefore, the main distinguishing feature for single scale models developed at this scale of organization is that they incorporate multiple microcommunities (i.e.…”

Optimal control analysis of hepatocytic-erythrocytic dynamics of Plasmodium falciparum malaria

“…An in-host P. falciparum malaria model is formulated to study optimal malaria control strategies within the human host. The deterministic model is an extension of the model in ( Orwa et al., 2018a ) and comprises of nine compartments of: (i) sporozoites ( S ), (ii) uninfected hepatocytes ( H ), (iii) infected hepatocytes ( X ), (iv) uninfected red blood cells ( R ), (v) early stage infected red blood cells (blood trophozoites, T ), (vi) mature infected red blood cells (blood schizonts, C ), (vii) merozoites ( M ), (viii) gametocytes ( G ) and (ix) CD8 + T cells ( Z ). The in-host malaria is subjected to a combination of malaria vaccine and anti-malarial drug control strategies.…”

Multiple-Strain Malaria Infection and Its Impacts on Plasmodium falciparum Resistance to Antimalarial Therapy: A Mathematical Modelling Perspective

“…The process of verification is however simpler. We can follow the steps as presented in [59, 60]. Let the total erythrocyte population C ( t ) evolve according to the following formulation:dCdt≤λx−μcC,where μ c =min{ μ x , μ ys , μ yr }.…”