Dynamics of Persistent Epidemic and Optimal Control of Vaccination

Masoud Saade (), Sebastian Aniţa and Vitaly Volpert
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Masoud Saade: S.M. Nikolsky Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia
Sebastian Aniţa: Faculty of Mathematics, University Alexandru Ioan Cuza, Bd. Carol I nr. 11, 700506 Iasi, Romania
Vitaly Volpert: S.M. Nikolsky Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia

Mathematics, 2023, vol. 11, issue 17, 1-15

Abstract: This paper is devoted to a model of epidemic progression, taking into account vaccination and immunity waning. The model consists of a system of delay differential equations with time delays determined by the disease duration and immunity loss. Periodic epidemic outbreaks emerge as a result of the instability of a positive stationary solution if the basic reproduction number exceeds some critical value. Vaccination can change epidemic dynamics, resulting in more complex aperiodic oscillations confirmed by some data on Influenza A in Norway. Furthermore, the measures of social distancing during the COVID-19 pandemic weakened seasonal influenza in 2021, but increased it during the next year. Optimal control allows for the minimization of epidemic cost by vaccination.

Keywords: delay epidemic model; vaccination; optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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