A 2-Dimensional Model for the Transmission Dynamics of Schistosomiasis in the Human-Snail Hosts

Abstract

The modes of transmission of schistosomiasis are considered. The transmission model is developed with an aim of establishing possible endemic equilibria within the community. Analysis of the model reveals that if the recovery rate β of human infectives and the death rate of snails δ are increased and if at the same time the contact rate κ of the human hosts with infested water is reduced, the disease gets eradicated from the community. Otherwise, the disease becomes endemic within the community which is a very much undesirable condition for the human population because of the debilitating nature of schistosomiasis. It is found out that this endemic state becomes stable if both the recovery rate β of human infectives and the death rate δ of snails are reduced. It can be made unstable by de-worming the human infectives and killing snails by use of molluscicides. Educating the community about the modes of transmission of the disease helps in reducing the contact rate with infested waters and hence disease prevention.