Viable controls in models for vector-borne diseases

Analysis of transient dynamic behaviour of controlled trajectories is a novel problem in the context of vector-borne diseases. Epidemiological modelling focuses often on investigation of local or global asymptotic stability of equilibria or on trajectories corresponding to optimal resource allocation if control is introduced. The study is motivated by the application of mosquito repellents as protective measure in textiles, paints and other household items. The model for a vector-borne disease is SIR for the host and SI for the vector with time-dependent controls. We determine the viability kernel comprising those initial states for the dynamical system such that the proportion of infected individuals is kept below a certain maximum level for all future times, and the respective viable trajectories. Analysis of viable controls has been done earlier for a SIS model for the host (DeLara & Salcedo 2016), which has properties of a quasi-monotone system. Our results (Rashkov 2021) extend the analysis to a more complex model system. We compute numerical approximations of the viability kernels and the viable trajectories using a variational framework.This work is partially supported by the Bulgarian National Science Fund within the National Science Program 'Petar Beron i NIE' [contract number KP-06-DB-5].