Abstract
A new deterministic model for ectoparasite‐borne diseases (which comprises four nonlinear coupled differential equations) is designed and analyzed. A full stability analysis of this model is investigated. First, the basic reproduction numbers ( , , and ) of the model are determined. The model has a locally and globally asymptotically stable disease‐free equilibrium point when . A unique infestation‐only boundary equilibrium point is shown to be globally asymptotically stable whenever by using a nonlinear Lyapunov function of Goh‐Volterra type, in conjunction with the LaSalle's invariance principle. On the other hand, the model has a unique globally asymptotically stable infected‐only boundary equilibrium point whenever . Moreover, the model has a unique endemic equilibrium point that is globally asymptotically stable provided that and . Finally, it is shown that replacing the mass incidence function with the standard incidence function in the ectoparasite‐borne diseases model with mass action incidence does not alter the qualitative dynamics of the model.
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