Continuous-time Predator-Prey-Like Systems of Non Linear Ordinary Differential Equations Linking Mosquito-Breeding Site Density to Community Action Under Temperature Effects

Abstract

\n A system of two first order nonlinear ordinary differential equations is used to model and theoretically investigate the dynamics of the formation of mosquito breeding sites in a uniform environment. The model captures the dynamic interplay between community action, climatic factors and the availability of mosquito breeding sites by interpreting the possible pathways and environmental processes leading to the formation of these breeding sites. The developed model is analysed using standard methods in nonlinear dynamical systems theory. Our results show that it is possible to attempt the problem of the dynamics of formation of breeding sites by taking into consideration the level of human consciousness as measured through human response to community action. Different feedback response functions are used to excite the breeding site removal and community action. For the case where the response functionals are both constants, we identify an indicator function whose size can indicate whether in the long run, community action can lead to the removal and elimination of breeding sites near human habitats. Using a predictor-corrector procedure that fits real climatic data to a continuous periodic function, we demonstrate how climatic variables can be included in the model and how models for the time variation of temperature and precipitation in a given area can be constructed just by appropriately choosing the parameters of a sinusoidal function and then correcting the output using nonlinear least squares analysis. Numerical simulation results are used to complement our analytical results.