Complex Dynamics in a Simple Malaria Model Stemming from the Interplay Between Incidence-Driven Human Behavior and Seasonality in the Infective Potential of a Mosquito Bite

Source abstract

We extend the classical Ross–Macdonald model for describing the spread of vector-borne diseases. First, we include spontaneous behavioral changes driven by the current and past information on the disease incidence. Second, we include seasonality in the infective potential of mosquito bites. This results in a hereditary model with distributed delay. We analytically investigate the general properties of both the disease-free equilibrium and the endemic equilibrium, in particular their local stability, and, for the DFE, we also show its global stability, even in the periodically forced model. We focused on two key scenarios: (i) a near-critical regime and (ii) a regime with a large basic reproduction number due to a large abundance of mosquitoes with respect to the human population. In the case of special memory kernels allowing a finite-dimensional reduction of the model, such as the Erlang kernels of orders 2 and 3, as well as the acquisition–fading kernel, we analytically and numerically investigate (i) the occurrence of oscillations of Yakubovich type in the autonomous model and (ii) the interplay between seasonality and behavior in the periodically forced model, and we show that this interplay can trigger nonlinear resonances and chaos.