Analysis of a Nonlinear System for Community Intervention in Mosquito Control

Non-linear difference equation models are employed in biology to describe the dynamics of certain populations and their interaction with the environment. In this paper we analyze a non-linear system describing community intervention in mosquito control through management of their habitats. The system takes the general form: { x_n+1 = ax_nh(py_n) + bh(qy _n) n = 0, 1,... y_n+1 = cx_n+ dy_n where the function h ∈ C¹([0, ∞) → [0, 1]) satisfying certain properties, will denote either h(t) = h₁(t) = e^-t and/or h(t) = h₂(t) = 1/(1 + t). We give conditions in terms of parameters for boundedness and stability. This enables us to explore the dynamics of prevalence/community-activity systems as affected by the range of parameters.