Continuous-time predator-prey-like systems used to investigate the question: Can human consciousness help eliminate temporary mosquito breeding sites from around human habitats?

Mosquito breeding-sites are an essential resource for mosquito growth, yet an understanding of their existence and creation, in the case of temporary habitats, have not been mathematically studied. Hence, we use a system of two first order nonlinear ordinary differential equations to model and theoretically investigate the dynamics of temporary mosquito breeding-sites formation in a uniform environment. The model captures the dynamic interplay between community action, climatic factors and availability of temporary mosquito breeding-sites by interpreting the possible pathways and environmental processes leading to temporary breeding-sites formation. Model’s analysis show it is possible to eliminate temporary breeding-sites from around a close vicinity to human habitats by increasing the level of human consciousness, with human consciousness measured via human response to community action. Different feedback response functions are used to excite breeding-site removal and community action. When the response functionals are both constants, an indicator function is identified, whose size can indicate whether in the long-run, community action can lead to the removal and elimination of temporary 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 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 showing the different dynamical behaviours that can be obtained. When breeding-site densities are high, human consciousness starts rising and its effect can lead to the reduction of breeding-site density, measured, and interpreted via community action. In some scenarios, the response can lead to complete removal of the breeding sites, while in others it may enter a limit cycle with different transient dynamics determined by the temperature parameters, waning rate of consciousness and breeding site impact on igniting consciousness. The novelty in this manuscript lies in the idea in which the focus is on modelling temporary mosquito breeding-sites, a process that is natural, yet neglected. Additionally, the incorporation of human consciousness highlights the need for a better understanding of human factors in neglected population dynamics studies and to attempt to correlate consciousness to adherence and its influence on disease control. Our mathematical model to address the problem of mosquito breeding-site formation, an important problem that has minimally been addressed, serves as a foundational model that can be extended to incorporate stochasticity in breeding site formation.