Modeling repellent-based interventions for control of vector-borne diseases with constraints on extent and duration

Peter Rashkov; Peter Rashkov

doi:10.3934/mbe.2022185

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 4: 4038-4061. doi: 10.3934/mbe.2022185

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Modeling repellent-based interventions for control of vector-borne diseases with constraints on extent and duration

Peter Rashkov ^,

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Akademik Georgi Bonchev, blok 8, 1113 Sofia, Bulgaria

Received: 10 September 2021 Revised: 21 January 2022 Accepted: 06 February 2022 Published: 15 February 2022

We study a simple model for a vector-borne disease with control intervention based on clothes and household items treated with mosquito repellents, which has constraints on the extent (population coverage) and on the time duration reflecting technological and physical properties. We compute first, the viability kernel of initial data of the model for which exists an optimal control that maintains the infected host population below a given cap for all future times. Second, we use the viability kernel to compute the set of initial data of the model for which exists an optimal control that brings this population below the cap in a time period not exceeding the intervention's duration. We discuss applications of this framework in predicting and evaluating the performance of control interventions under the given type of constraints.
- vector-borne diseases,
- cooperative system,
- optimal control,
- viability,
- reachability
Citation: Peter Rashkov. Modeling repellent-based interventions for control of vector-borne diseases with constraints on extent and duration[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 4038-4061. doi: 10.3934/mbe.2022185

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Abstract

We study a simple model for a vector-borne disease with control intervention based on clothes and household items treated with mosquito repellents, which has constraints on the extent (population coverage) and on the time duration reflecting technological and physical properties. We compute first, the viability kernel of initial data of the model for which exists an optimal control that maintains the infected host population below a given cap for all future times. Second, we use the viability kernel to compute the set of initial data of the model for which exists an optimal control that brings this population below the cap in a time period not exceeding the intervention's duration. We discuss applications of this framework in predicting and evaluating the performance of control interventions under the given type of constraints.

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