Dynamics of Persistent Epidemic and Optimal Control of Vaccination
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 i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/17/3770 |
| _version_ | 1797582149689278464 |
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| author | Masoud Saade Sebastian Aniţa Vitaly Volpert |
| author_facet | Masoud Saade Sebastian Aniţa Vitaly Volpert |
| author_sort | Masoud Saade |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T23:17:57Z |
| format | Article |
| id | doaj.art-e93a735ab2d5454b8b57c109f86bc123 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:17:57Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e93a735ab2d5454b8b57c109f86bc1232023-11-19T08:31:57ZengMDPI AGMathematics2227-73902023-09-011117377010.3390/math11173770Dynamics of Persistent Epidemic and Optimal Control of VaccinationMasoud Saade0Sebastian Aniţa1Vitaly Volpert2S.M. Nikolsky Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, RussiaFaculty of Mathematics, University Alexandru Ioan Cuza, Bd. Carol I nr. 11, 700506 Iasi, RomaniaS.M. Nikolsky Mathematical Institute, Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, RussiaThis 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.https://www.mdpi.com/2227-7390/11/17/3770delay epidemic modelvaccinationoptimal control |
| spellingShingle | Masoud Saade Sebastian Aniţa Vitaly Volpert Dynamics of Persistent Epidemic and Optimal Control of Vaccination Mathematics delay epidemic model vaccination optimal control |
| title | Dynamics of Persistent Epidemic and Optimal Control of Vaccination |
| title_full | Dynamics of Persistent Epidemic and Optimal Control of Vaccination |
| title_fullStr | Dynamics of Persistent Epidemic and Optimal Control of Vaccination |
| title_full_unstemmed | Dynamics of Persistent Epidemic and Optimal Control of Vaccination |
| title_short | Dynamics of Persistent Epidemic and Optimal Control of Vaccination |
| title_sort | dynamics of persistent epidemic and optimal control of vaccination |
| topic | delay epidemic model vaccination optimal control |
| url | https://www.mdpi.com/2227-7390/11/17/3770 |
| work_keys_str_mv | AT masoudsaade dynamicsofpersistentepidemicandoptimalcontrolofvaccination AT sebastiananita dynamicsofpersistentepidemicandoptimalcontrolofvaccination AT vitalyvolpert dynamicsofpersistentepidemicandoptimalcontrolofvaccination |