Optimal control of a reaction-diffusion epidemic model with non-compliance
In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioural effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a portion of the population does not comply with them, and this...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
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| Series: | European Journal of Applied Mathematics |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S0956792525000130/type/journal_article |
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| Summary: | In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioural effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a portion of the population does not comply with them, and this non-compliance affects the spread of the disease. Drawing from social contagion theory, our model allows for the spread of non-compliance parallel to the spread of the disease. The quantities of interest for control are the reduction in infection rate among the compliant population, the rate of spread of non-compliance and the rate at which non-compliant individuals become compliant after, e.g., receiving more or better information about the underlying disease. We prove the existence of global-in-time solutions for fixed controls and study the regularity properties of the resulting control-to-state map. The existence of optimal control is then established in an abstract framework for a fairly general class of objective functions. Necessary first–order optimality conditions are obtained via a Lagrangian-based stationarity system. We conclude with a discussion regarding minimisation of the size of infected and non-compliant populations and present simulations with various parameters values to demonstrate the behaviour of the model. |
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| ISSN: | 0956-7925 1469-4425 |