Mathematical modelling of the in-host dynamics of malaria and the effects of treatment

Abstract

Malaria research and mathematical models have mainly concentrated on malaria Plasmodium at the blood stage. This has left many questions concerning models of parasite dynamics in the liver and within the mosquito. These concerns are anticipated to keep scientists busy trying to understand the biology of the parasite for some more years to come. Thorough knowledge of parasite biology helps in designing appropriate drugs targeting particular stages of Plasmodium. To achieve this, there is need to study the transmission dynamics of malaria and the interaction between the infection in the liver, blood and mosquito using a mathematical model. In this study, a within-host mathematical model is proposed and considers the dynamics of P. falciparum malaria from the liver to the blood in the human host and then to the mosquito. Several techniques, including center manifold theory and sensitivity analysis are used to understand relevant features of the model dynamics like basic reproduction number, local and global stability of the disease-free equilibrium and conditions for existence of the endemic equilibrium. Results indicate that the infection rate of merozoites, the rate of sexual reproduction in gametocytes, burst size of both hepatocytes and erythrocytes are more sensitive parameters for the onset of the disease. However, a treatment strategy using highly effective drugs against such parameters can reduce on malaria progression and control the disease. Numerical simulations show that drugs with an efficacy above 90% boost healthy cells, reduce infected cells and clear parasites in human host. Therefore more needs to be done such as research in parasite biology and using highly effective drugs for treatment of malaria.

Mathematical Model for Hepatocytic-Erythrocytic Dynamics of Malaria

“…Malaria infection dynamics are most rapid in the first 2 weeks within the host liver as illustrated in Figures 4(a), 4(b), and 4(c). This is similar to results in [22,31]. In the absence of clinical intervention, some of the sporozoites may remain dormant in the human liver and could cause future malaria infections.…”

“…Although the models in [19,21,23,30] have considered the impact of immune response and treatment, the modelling is only limited to the blood stage of Plasmodium falciparum development. In [20,22,31], the liver stage is incorporated in the malaria model. However, the contribution of immune system is ignored in [20,31].…”

“…In [20,22,31], the liver stage is incorporated in the malaria model. However, the contribution of immune system is ignored in [20,31]. Moreover, all the immune cells are assumed to play an active role during malaria infection in [22].…”

Mathematical modeling of climate change and malaria transmission dynamics: a historical review

“…The complex within-host dynamics of human Plasmodium infection, how these affect the efficacy of treatment and control measures, and their interaction with the immune response, have been the focus of multiple modeling works, e.g. (Teboh-Ewungkem et al 2010;Li et al 2011;Gurarie et al 2012;Eckhoff 2012;Demasse and Ducrot 2013;Childs and Buckee 2015;Childs and Prosper 2017;Tabo et al 2017). However, to our knowledge no climate-focused models have focused deeply upon these within-host dynamics, although it is likely that such work is needed to fully elucidate how climate change might affect malaria epidemiology and control efforts in the future (see also Sect.…”

“…Coupling an explicit model for the within-host dynamics of malaria (principally the within-host immune response) to its epidemiology is a fundamental challenge. Indeed, even describing the within-host dynamics mathematically in a way the reproduces the qualitative dynamics of long-term infection has proven most difficult, and this issue has its own extensive literature that it is beyond the scope of this paper, although a very partial reference list includes Teboh-Ewungkem et al (2010), Li et al (2011), Saralamba et al (2011), Gurarie et al (2012), Eckhoff (2012, Demasse and Ducrot (2013), Childs and Buckee (2015), Childs and Prosper (2017), Tabo et al (2017), and a recent work by Childs and Buckee (2015) highlights the problems of accurately modeling within-host dynamics in some depth. Since these dynamics may interact in unexpected ways with malaria epidemiology (Childs and Buckee 2015), a complete understanding of climate and malaria will likely necessitate a deeper consideration of the in-host stages than has heretofore been attempted.…”