Modeling and analysis of bilharzia disease

Abstract

In this paper the dynamics of bilharazia disease in the humans, which represents its main host, is formulated mathematically. The proposed system is studied analytically. The local stability is investigated for all possible equilibrium points.  Using suitable Lyapunov functions the basin of attraction of each point is specified. The conditions of occurring local bifurcation in the system are established. Numerical simulations are performed to study the global dynamics of the system and specify the set of control parameters. It is observed that the system has no periodic dynamics and the disease is controlled under some conditions on the parameters.

Keywords: Bilharzia; Parasite disease; Stability; Local bifurcation.