Mathematical Modelling of the Dynamics of the Spread of Schistosomiasis Incorporating Protection of Humans

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International Journal of Recent Research in Mathematics Computer Science and Information Technology


Schistosomiasis, also known as Bilharziasis, is a parasitic disease of global concern, and is among the neglected tropical diseases. It is caused by the digenetic trematode flukes of the genus Schistosoma and transmitted by fresh water snails of the family Planorbidae. Its clinical manifestation depends on the immunity of the person, the warm burden and the duration of the same worms in the body. African countries suffer greatly from this disease. We have formulated a mathematical model with four compartments, Susceptible-Protected-Infected-Treated, (SPIT), and the corresponding ordinary differential equations in an attempt to investigate the impact of human protection. The disease free equilibrium and endemic equilibrium have been analyzed. The stability of the disease free equilibrium has also been determined. The reproduction number has been determined using the next Generation matrix. Mathematical simulation was carried out. The impact of human protection on the dynamics of the spread of the disease has been analyzed. Our results show that protection of the human being plays a great role in controlling the spread of this disease. It contributes significantly to reduction of infections and the stability of the susceptible population.




Schistosomiasis modeling, Mathematical modeling, Reproduction number.