Modeling and stability analysis of cryptosporidiosis transmission dynamics with Beddington-Deangelis incidence

Abstract

In this paper, a model describing the dynamics of Cryptosporidiosis is developed and analysed using ordinary differential equations with a non linear incidence called Beddington-DeAngelis function. We computed the basic reproduction number (R_ha) using the next generation matrix method and carry out the stability analysis of the model equilibria. We applied the center manifold theory to investigate the local stability of the endemic equilibrium and found that the model exhibits a forward bifurcation at R_ha=1. Further, the global stability of the endemic equilibrium is obtained under a certain condition using Lyapunov’s method and LaSalle’S invariance principle. The most sensitive parameters on the model outcome are also identified using the normalized forward sensitivity index. Finally, we performed numerical simulations and displayed then graphically to validate our analytical results, and the epidemiological implications of the key out comes were briefly discussed.