From Age-Structured Trophic Networks to Applied Control : Stabilization and Harvesting Strategies for Non-Transitive Competition and the Dynamics of Mosquitoes

Abstract: We propose and analyze a nonlinear age-structured multi-species model that serves as a unifying framework for ecological and biotechnological systems in complex environments (microbial communities, bioreactors, etc.). The formulation incorporates nonlocal intra- and interspecific interactions modulated by environmental covariates; under general assumptions on mortality, reproduction rates and interaction kernels, we establish existence, uniqueness and positivity of solutions. We illustrate the model's practical relevance along two lines: (i) multi-species examples, notably a non-transitive (cyclic) competition model, for which we show that, under the model assumptions, a control applied to a single species can achieve global stabilization of the system; furthermore, verification of the Kalman condition in this context provides an essential theoretical prerequisite and highlights that this single control acts indirectly on all other species; and (ii) the population dynamics of malaria-vector mosquitoes, for which we develop two control strategies (biological and genetic) and, in the biological-control scenario, prove global asymptotic stability of the aquatic compartment by constructing an explicit Lyapunov function. Numerical simulations validate the theoretical results and compare the effectiveness of the proposed strategies in reducing vector density and malaria transmission.