Stochastic near-optimal controls for treatment and vaccination in a COVID-19 model with transmission incorporating Lévy jumps

Abstract

The COVID-19 pandemic has triggered a groundbreaking reliance on mathematical modelling as an important tool for studying and managing the spread of the virus since its emergence. Public health preventive measures such as vaccination and therapeutics can effectively reduce or eradicate an infectious disease. This work investigates these two strategies for controlling the COVID-19 epidemic through a stochastic epidemiological modelling approach. The existence and uniqueness of a positive solution of the stochastic system is studied. A priori estimates of the vaccination and treatment controls are established. Sufficient and necessary conditions are obtained for the near-optimal control problem of the stochastic model using the maximum condition of the Hamiltonian function and the Ekeland principle. Finally, to support our theoretical results, numerical simulations for a combination of optimized vaccination and treatment strategies were presented to understand the challenges posed by COVID-19 in Brazil.

Keywords:

• COVID-19 model
• Lévy process
• near-optimal control
• stochastic control
• adjoint process

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

We gratefully acknowledge the financial support provided by the Ministerio de Ciencia e Innovación (Spain) and http://dx.doi.org/10.13039/501100002924FEDER (European Community) under grant PID2021-122991NB-C21. Additionally, we extend our sincere appreciation to the Erasmus+ project facilitated between Linnaeus University, Växjö, Sweden, and Ibn Tofail University, Kénitra, Morocco, under grant number 2023-1-SE01-KA171-HED-000131891 for their valuable collaboration.