Modelling Biomedical Systems Research Group, Department of Applied Mathematics, National University of Science and Technology, P.O. Box AC 939 Ascot, Bulawayo, Zimbabwe
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Schistosomiasis infection is characterized by the presence of adult worms in the portal and mesenteric veins of humans as part of a complex migratory cycle initiated by cutaneous penetration of the cercariae shed by infected freshwater snails. The drug praziquantel is not always effective in the treatment against schistosomiasis at larvae stage. However, our simulations show that it is effective against mature worms and eggs. As a result, the study and understanding of immunological responses is key in understanding parasite dynamics. We therefore introduce quantitative interpretations of human immunological responses of the disease to formulate mathematical models for the within-host dynamics of schistosomiasis. We also use numerical simulations to demonstrate that it is the level of T cells that differentiates between either an effective immune response or some degree of infection. These cells are responsible for the differentiation and recruitment of eosinophils that are instrumental in clearing the parasite. From the model analysis, we conclude that control of infection is much attributed to the value of a function f, a measure of the average number of larvae penetrating a susceptible individual having hatched from an egg released by an infected individual. This agrees with evidence that there is a close association between the ecology, the distribution of infection and the disease.