Global stability analysis of a general nonlinear scabies dynamics model

Abstract

Abstract In this work we present a general nonlinear model of scabies infection dynamics. The dynamics is described by a five-dimensional system of ordinary differential equations that expresses the transmissions between susceptible, infectious/infective individuals and adult scabiei mites. The intrinsic growth rate for susceptible individuals, the infection rates as well as the removal and transmission rates of infected individuals and adult mites are modeled by general nonlinear functions. Based on a set of conditions on these general functions we investigate and analyze our model. Nonnegativity and boundedness of solutions of the model are conducted. A basic reproduction number, ℜ 0 M , is calculated for the model which ensures the existence and stability of all corresponding equilibria. Using candidate Lyapunov functions, it is shown that whenever the basic reproduction number is less than or equal unity, the model has an associated disease-free equilibrium, Q 0 M , that is globally asymptotically stable. In addition, when the threshold exceeds unity the model has a globally asthmatically stable endemic equilibrium, Q ¯ M . Finally, using some parameter values related to the scabies infection dynamics, numerical simulation results are demonstrated to clarify the strength of our main theoretical results. Sensitivity analysis of the endemic equilibrium has been performed.