Dynamics of human schistosomiasis model with hybrid miracidium and cercariae

•We proposed a original mathematical model for the synergistic interaction between two parental strains of schistosomiasis and their hybrid strains.•The global dynamic of each sub-model is completely determined.•the basic reproduction number of the model plays an important role for eradication of the disease.•We propose suggestions concerning snail in order to control the disease.•Our results imply that controlling snails in the water should be effective in order to control the transmission of schistosomiasis. Hybridization between schistosomes under laboratory conditions has been shown to result in heterosis (higher fecundity, faster maturation time, wider intermediate host spectrum), having important implications on disease prevalence, pathology and treatment. This paper addresses the synergistic interaction between two parental strains of schistosomiasis and their hybrid strain using a deterministic model, which incorporates many of the essential biological and epidemiological features of the disease. The full model is divided into four sub-models and the global dynamic of each sub-model is completely determined. Our analysis reveals that the basic reproduction number of the model plays an important role for eradication of the disease. Moreover, there exist a critical interval of the rate of virulence of hybrid miracidium on snails in which the hybrid strain dominate parental strains and proliferate in the population. Numerical simulations support our analytical conclusions, imply that controlling snails in the water should be effective in order to control the transmission of schistosomiasis.