Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model
Abstract Background Facing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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BMC
2022-06-01
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| Series: | BMC Infectious Diseases |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s12879-022-07403-5 |
| _version_ | 1811258237434986496 |
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| author | Naoya Fujiwara Tomokatsu Onaga Takayuki Wada Shouhei Takeuchi Junji Seto Tomoki Nakaya Kazuyuki Aihara |
| author_facet | Naoya Fujiwara Tomokatsu Onaga Takayuki Wada Shouhei Takeuchi Junji Seto Tomoki Nakaya Kazuyuki Aihara |
| author_sort | Naoya Fujiwara |
| collection | DOAJ |
| description | Abstract Background Facing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs is that different NPIs have been implemented at different times based on the situation of each country; therefore, few assumptions can be shared about how the introduction of policies affects the patient population. Mathematical models can contribute to further understanding these phenomena by obtaining analytical solutions as well as numerical simulations. Methods and results In this study, an NPI was introduced into the SIR model for a conceptual study of infectious diseases under the condition that the transmission rate was reduced to a fixed value only once within a finite time duration, and its effect was analyzed numerically and theoretically. It was analytically shown that the maximum fraction of infected individuals and the final size could be larger if the intervention starts too early. The analytical results also suggested that more individuals may be infected at the peak of the second wave with a stronger intervention. Conclusions This study provides quantitative relationship between the strength of a one-shot intervention and the reduction in the number of patients with no approximation. This suggests the importance of the strength and time of NPIs, although detailed studies are necessary for the implementation of NPIs in complicated real-world environments as the model used in this study is based on various simplifications. |
| first_indexed | 2024-04-12T18:10:17Z |
| format | Article |
| id | doaj.art-9227714be92045d78062c875cd889090 |
| institution | Directory Open Access Journal |
| issn | 1471-2334 |
| language | English |
| last_indexed | 2024-04-12T18:10:17Z |
| publishDate | 2022-06-01 |
| publisher | BMC |
| record_format | Article |
| series | BMC Infectious Diseases |
| spelling | doaj.art-9227714be92045d78062c875cd8890902022-12-22T03:21:51ZengBMCBMC Infectious Diseases1471-23342022-06-0122111110.1186/s12879-022-07403-5Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic modelNaoya Fujiwara0Tomokatsu Onaga1Takayuki Wada2Shouhei Takeuchi3Junji Seto4Tomoki Nakaya5Kazuyuki Aihara6Graduate School of Information Sciences, Tohoku UniversityGraduate School of Information Sciences, Tohoku UniversityDepartment of Microbiology, Graduate School of Human Life and Ecology, Osaka Metropolitan UniversityFaculty of Nursing and Nutrition, University of NagasakiDepartment of Microbiology, Yamagata Prefectural Institute of Public HealthGraduate School of Environmental Studies, Tohoku UniversityInternational Research Center for Neurointelligence, The University of TokyoAbstract Background Facing a global epidemic of new infectious diseases such as COVID-19, non-pharmaceutical interventions (NPIs), which reduce transmission rates without medical actions, are being implemented around the world to mitigate spreads. One of the problems in assessing the effects of NPIs is that different NPIs have been implemented at different times based on the situation of each country; therefore, few assumptions can be shared about how the introduction of policies affects the patient population. Mathematical models can contribute to further understanding these phenomena by obtaining analytical solutions as well as numerical simulations. Methods and results In this study, an NPI was introduced into the SIR model for a conceptual study of infectious diseases under the condition that the transmission rate was reduced to a fixed value only once within a finite time duration, and its effect was analyzed numerically and theoretically. It was analytically shown that the maximum fraction of infected individuals and the final size could be larger if the intervention starts too early. The analytical results also suggested that more individuals may be infected at the peak of the second wave with a stronger intervention. Conclusions This study provides quantitative relationship between the strength of a one-shot intervention and the reduction in the number of patients with no approximation. This suggests the importance of the strength and time of NPIs, although detailed studies are necessary for the implementation of NPIs in complicated real-world environments as the model used in this study is based on various simplifications.https://doi.org/10.1186/s12879-022-07403-5Infectious diseasesPandemicsNon-pharmaceutical interventionsHybrid dynamical systems |
| spellingShingle | Naoya Fujiwara Tomokatsu Onaga Takayuki Wada Shouhei Takeuchi Junji Seto Tomoki Nakaya Kazuyuki Aihara Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model BMC Infectious Diseases Infectious diseases Pandemics Non-pharmaceutical interventions Hybrid dynamical systems |
| title | Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model |
| title_full | Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model |
| title_fullStr | Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model |
| title_full_unstemmed | Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model |
| title_short | Analytical estimation of maximum fraction of infected individuals with one-shot non-pharmaceutical intervention in a hybrid epidemic model |
| title_sort | analytical estimation of maximum fraction of infected individuals with one shot non pharmaceutical intervention in a hybrid epidemic model |
| topic | Infectious diseases Pandemics Non-pharmaceutical interventions Hybrid dynamical systems |
| url | https://doi.org/10.1186/s12879-022-07403-5 |
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