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Schistosomiasis is a chronic ill-health disease with the infection acquired when schisto- somes,thelarvalform(cercaria)ofparasiticbloodflukesfromfreshwaterpenetrate into human body and live in the blood vessel. According to WHO recent report on thedisease,240millionpeopleisinfectedwiththediseaseintheworldwithover700 millionpeoplelivinginendemicareas.ReportsalsoshowthatNigeriahasthehighest casesofschistosomiasisintheworldwithover30millionexpectedtobetreatedevery year.Severaldeterministicpopulationmodelshavebeenformulatedintheliterature to study the dynamics of schistosomiasis in human, snails and the parasitespopula- tion,butnonehasconsideredtheimpactofcasedetectiononschistosomiasisdisease transmissiondynamicstothebestofourknowledge.
Inthisstudy,wepresentanonlinearmathematicalmodeltoprovidemathematical andepidemiologicalviewtotheeffectofcasedetectiononthetransmissiondynamics of schistosomiasis. The qualitative properties of the model as well as the local and global asymptotic stability of equilibria were established. Bifurcation analysis was carried out to test for the existence of backward bifurcation. Furthermore, the disease free equilibrium of the model was shown to be globally asymptotically stable (GAS)whenevertherelatedreproductionnumber, ,islessthanunity;thisimplies that schistosomiasis cannot prevail in the population. Moreover, we established the globalasymptoticstabilityoftheendemicequilibriumwhentheassociatedreproduction number is greater than one. This suggests that schistosomiasis will prevail in the population.
Numericalsimulationsofthemodelshowedtheeffectofvaryingsomeparameters ofthemodelonthepopulationdynamicsofschistosomiasis.
