Human malaria


We develop models to describe the within-host dynamics of different plasmodi such as P. falciparum, P. Vivax or P. Malariae. For the parasitized stage of red blood cells (RBCs), we consider an age-structured dynamics, where the age is a continuous variable representing the time since the concerned RBC is parasitized. Such a continuous age structure allow to track the maturity and the different stages of sequestrated parasites, but also to have a refined description of the parasitized RBC rupture and of the merozoites release phenomenon (Djidjou-Demasse & Ducrot). Further, such a model easily allows to include anti-malarial treatments acting on some particular stages of the development of the parasites into the parasitized RBCs. Using gametocyte production as a proxy variable of infectiousness, we found the age-structured model to perform best in representing the gametocyte dynamics compared to the classical K-compartments of ordinary differential equations (Djidjou-Demasse et al.).


At the epidemiological level, we are also developing malaria transmission models with seasonal mosquito life-history traits such as: periodic-mosquitoes per capita birth rate, -mosquitoes death rate, -probability of mosquito to human disease transmission, -probability of human to mosquito disease transmission and -mosquitoes biting rate. In addition to some interesting math results, the model outputs are in accordance with the seasonal variation of the reported cases of a malaria-epidemic region, e.g., in Mpumalanga province in South Africa (Djidjou-Demasse et al.).


In contrast to the many theoretical studies on the transmission of human-mosquitoes malaria infection, few studies have considered multiple structure model formulations including (i) the chronological age of humans and mosquitoes population, (ii) the time since humans and mosquitoes are infected and (iii) humans waning immunity (i.e., the progressive loss of protective antibodies after recovery). Such structural variables are well documented to be fundamental for the transmission of human-mosquitoes malaria infections. Eg, the expression of the basic reproduction number obtained here particularly highlight the effect of the above structural variables on key important epidemiological traits of the human-vector association. This includes the vectorial capacity (i.e., vector’s daily reproduction rate), humans transmission probability and survival rates. (Richard et al.).