Analysis and solutions of generalized Chagas vectors re-infestation model of fractional order type

Abstract

• A generalized Chagas vectors re-infestation model of fractional order type is proposed. • Our model considers insecticide treatment as continuous spraying where the spraying rate depends on the rate of detection of infestation and time lag between detection and application of insecticide. • Existence and uniqueness results of solutions are proven. • We prove local and global stability of the proposed model and obtain conditions for unique endemic equilibrium. • The effects of the fractional order and key parameters on the proposed model are examined from the numerical analysis results. • Based on the results obtained, we provide some recommendations useful to better understand and reduce the re-infestation of Chagas disease. Trypanosoma cruzi is the parasite that causes Chagas disease in which Triatomine bugs, a type of reduviid bug, are the carrier. Insecticide spraying is one of the most common measures to reduce triatomine infestation. In this paper, we propose a generalized Chagas vectors re-infestation model of fractional order type. This fractional model has been developed to study insecticide-based strategies for controlling vectors of Chagas disease. Our model considers insecticide treatment as continuous spraying where the spraying rate depends on the rate of detection of infestation and time lag between detection and application of insecticide. We incorporate two spraying rates, r (triatomines detection and only infected housing units are treated with deltamethrin insecticide) and r o (other insects detection and treatment is applied to all units). Existence and uniqueness results of solutions are proven. We prove local and global stability of the proposed model and obtain conditions for unique endemic equilibrium. Our numerical results exposed the intrinsic properties of the model using fractional derivative . Based on our results, triatomines infestation cannot be eradicated when there is migration from the sylvatic areas, control strategies aimed at reducing infestation from the sylvatic areas are highly recommended.