Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies
In this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non control...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-11-01
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| Series: | Computational and Mathematical Biophysics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/cmb-2022-0143 |
| _version_ | 1797947776832634880 |
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| author | Chhetri Bishal Vamsi D. K. K. Prakash D. Bhanu Balasubramanian S. Sanjeevi Carani B. |
| author_facet | Chhetri Bishal Vamsi D. K. K. Prakash D. Bhanu Balasubramanian S. Sanjeevi Carani B. |
| author_sort | Chhetri Bishal |
| collection | DOAJ |
| description | In this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non controlled model and calculate the basic reproduction number and do the stability analysis. We then formulate an optimal control problem with vaccination and treatment as control variables and study the same. Pontryagin’s Minimum Principle is used to obtain the optimal vaccination and treatment rates. Optimal vaccination and treatment policies are analysed for different values of the weight constant associated with the cost of vaccination and different efficacy levels of vaccine. Findings from these suggested that the combined strategies (vaccination and treatment) worked best in minimizing the infection and disease induced mortality. In order to reduce COVID-19 infection and COVID-19 induced deaths to maximum, it was observed that optimal control strategy should be prioritized to the population with age greater than 40 years. Varying the cost of vaccination it was found that sufficient implementation of vaccines (more than 77 %) reduces the size of COVID-19 infections and number of deaths. The infection curves varying the efficacies of the vaccines against infection were also analysed and it was found that higher efficacy of the vaccine resulted in lesser number of infections and COVID induced deaths. The findings would help policymakers to plan effective strategies to contain the size of the COVID-19 pandemic. |
| first_indexed | 2024-04-10T21:32:01Z |
| format | Article |
| id | doaj.art-bc9ae66d6d4f4280980dddfe8156f871 |
| institution | Directory Open Access Journal |
| issn | 2544-7297 |
| language | English |
| last_indexed | 2024-04-10T21:32:01Z |
| publishDate | 2022-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Computational and Mathematical Biophysics |
| spelling | doaj.art-bc9ae66d6d4f4280980dddfe8156f8712023-01-19T13:20:29ZengDe GruyterComputational and Mathematical Biophysics2544-72972022-11-0110128130310.1515/cmb-2022-0143Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment StrategiesChhetri Bishal0Vamsi D. K. K.1Prakash D. Bhanu2Balasubramanian S.3Sanjeevi Carani B.4Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, IndiaDepartment of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, IndiaDepartment of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, IndiaDepartment of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, IndiaVice-Chancellor, Sri Sathya Sai Institute of Higher Learning, India; Department of Medicine, Karolinska Institute, Stockholm, SwedenIn this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non controlled model and calculate the basic reproduction number and do the stability analysis. We then formulate an optimal control problem with vaccination and treatment as control variables and study the same. Pontryagin’s Minimum Principle is used to obtain the optimal vaccination and treatment rates. Optimal vaccination and treatment policies are analysed for different values of the weight constant associated with the cost of vaccination and different efficacy levels of vaccine. Findings from these suggested that the combined strategies (vaccination and treatment) worked best in minimizing the infection and disease induced mortality. In order to reduce COVID-19 infection and COVID-19 induced deaths to maximum, it was observed that optimal control strategy should be prioritized to the population with age greater than 40 years. Varying the cost of vaccination it was found that sufficient implementation of vaccines (more than 77 %) reduces the size of COVID-19 infections and number of deaths. The infection curves varying the efficacies of the vaccines against infection were also analysed and it was found that higher efficacy of the vaccine resulted in lesser number of infections and COVID induced deaths. The findings would help policymakers to plan effective strategies to contain the size of the COVID-19 pandemic.https://doi.org/10.1515/cmb-2022-0143covid-19age structurevaccine efficacyvaccination coverageoptimal control problem92bxx92d3049-xx34-xx |
| spellingShingle | Chhetri Bishal Vamsi D. K. K. Prakash D. Bhanu Balasubramanian S. Sanjeevi Carani B. Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies Computational and Mathematical Biophysics covid-19 age structure vaccine efficacy vaccination coverage optimal control problem 92bxx 92d30 49-xx 34-xx |
| title | Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies |
| title_full | Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies |
| title_fullStr | Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies |
| title_full_unstemmed | Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies |
| title_short | Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies |
| title_sort | age structured mathematical modeling studies on covid 19 with respect to combined vaccination and medical treatment strategies |
| topic | covid-19 age structure vaccine efficacy vaccination coverage optimal control problem 92bxx 92d30 49-xx 34-xx |
| url | https://doi.org/10.1515/cmb-2022-0143 |
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