Dynamics of Infected Snails and Mated Schistosoma Worms within the Human Host

Male and female worms are independently distributed within a human host each with a Poisson probability distribution mass function. Mating takes place immediately when partners are available. It was found that the mated worm function is non-linear near the origin and becomes almost linear as the worms increase. They increase with increase in the worm load due to aggregation of worms. This also increases the infection of snails which are secondary hosts. On the analysis of the model, three equilibrium states were found, two of which were stable and one unstable. A stable endemic equilibrium within a community is very much undesirable. So the main objective of the model was to have the point O(0,0) as the only equilibrium point. This is a situation where there are no worms within the human host and the environment is free of infected snails. A critical point, above which the disease would be chronic and below which the disease would be eradicated, was found and analyzed. The parameters indicated that to achieve a disease free environment, the death rate of worms within the human host should be much greater than the cercariae that penetrate the human. Also the death rate of infected snails should be much higher than the contact rate between the miracidia and the snails. It was concluded that de-worming and killing of snails should be emphasized for disease control and educating the masses on the modes of disease transmission is quite necessary for prevention of the disease.