STABILITY ANALYSIS OF THEILERIOSIS INFECTION WITH ISOLATION

T.S. Faniran, A.A. Waheed, B. Adebo

Abstract


Theileriosis is an infectious disease in cattle caused by theileria annulata,carried by ticks of the genius Hyalomma. A mathematical representation ofcompartmental model for theileriosis transmission in cattle host and tick vector is formulated.The model incorporates a new class of isolated cattle in the cattle population.Isolated cattle are those that are infected with theileriosis but isolated to prevent furtherinfection. The stability of the model is analysed for the existence of the disease-freeand endemic equilibrium points. The basic reproduction number, R0, is determinedrespectively. It is shown that theileriosis infection dies out of cattle population andconverges to disease-free equilibrium point if R0 < 1. But if R0 > 1, then the diseasepersists in the population and converges to endemic equilibrium point.

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