Optimal control of an epidemic model with treatment in the presence of media coverage
During large scale outbreaks of infectious diseases, it is imperative that media report about the potential risks. Because media reporting plays a vital role in disseminating crucial information about diseases and its associated risk, understanding how media reports could influence individuals’ beha...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-06-01
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| Series: | Scientific African |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468227624000838 |
| _version_ | 1797289759948668928 |
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| author | Mamadou L. Diagne Folashade B. Agusto Herieth Rwezaura Jean M. Tchuenche Suzanne Lenhart |
| author_facet | Mamadou L. Diagne Folashade B. Agusto Herieth Rwezaura Jean M. Tchuenche Suzanne Lenhart |
| author_sort | Mamadou L. Diagne |
| collection | DOAJ |
| description | During large scale outbreaks of infectious diseases, it is imperative that media report about the potential risks. Because media reporting plays a vital role in disseminating crucial information about diseases and its associated risk, understanding how media reports could influence individuals’ behavior and its potential impact on disease transmission dynamics is important. A mathematical model within an optimal control framework of a generic disease, accounting for treatment and media reporting of disease-induced deaths is formulated. Due to the complexity of choosing the best media function, our goal is to attempt to address the following research question: what is the effect of the media-induced functional response on mitigating the spread of the disease? Connecting the functional forms to the control problem is an approach that is not very developed in the literature. Thus, this study analyses the effect of different incidence functions on disease transmission, and the qualitative nature of epidemic dynamics by carrying out optimal control analysis using three different contact rates and a media function that is dependent on the number of deaths. Theoretical analyses show that the functional forms of the effective contact rate have no effect on initial disease transmission. Time-dependent controls for treatment and vaccination with a constant effective contact rate are incorporated to determine optimal control strategies. Numerical simulations show the short-term impact of media coverage on mitigating the spread of the disease, and it is observed that with three incidence functions used, the qualitative nature of the controls remains the same. The effective contact rates are graphically shown to have a population-level effect on the disease dynamics as the number of treated and recovered individuals could be significantly different. Finally, it is shown that treatment of infectives should be at its maximum rate for a longer period compared to vaccination, while concurrent implementation of vaccination and treatment is more impactful in mitigating the spread of the disease. Thus, it is imperative that media reports and health policy decision making on infectious diseases are contextualized. |
| first_indexed | 2024-03-07T19:09:36Z |
| format | Article |
| id | doaj.art-a9c3c55442bb4ecbb73c072ecc0c5e00 |
| institution | Directory Open Access Journal |
| issn | 2468-2276 |
| language | English |
| last_indexed | 2024-03-07T19:09:36Z |
| publishDate | 2024-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Scientific African |
| spelling | doaj.art-a9c3c55442bb4ecbb73c072ecc0c5e002024-03-01T05:06:55ZengElsevierScientific African2468-22762024-06-0124e02138Optimal control of an epidemic model with treatment in the presence of media coverageMamadou L. Diagne0Folashade B. Agusto1Herieth Rwezaura2Jean M. Tchuenche3Suzanne Lenhart4Département de Mathématiques, UFR des Sciences et Technologies, Université de Thiès, Thiès, Senegal; Corresponding author.Department of Ecology & Evolutionary Biology, University of Kansas, Lawrence, KS, USAMathematics Department, University of Dar es Salaam, P.O. Box 35062, Dar es Salaam, TanzaniaSchool of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, South AfricaDepartment of Mathematics, University of Tennessee, Knoxville, TN, USADuring large scale outbreaks of infectious diseases, it is imperative that media report about the potential risks. Because media reporting plays a vital role in disseminating crucial information about diseases and its associated risk, understanding how media reports could influence individuals’ behavior and its potential impact on disease transmission dynamics is important. A mathematical model within an optimal control framework of a generic disease, accounting for treatment and media reporting of disease-induced deaths is formulated. Due to the complexity of choosing the best media function, our goal is to attempt to address the following research question: what is the effect of the media-induced functional response on mitigating the spread of the disease? Connecting the functional forms to the control problem is an approach that is not very developed in the literature. Thus, this study analyses the effect of different incidence functions on disease transmission, and the qualitative nature of epidemic dynamics by carrying out optimal control analysis using three different contact rates and a media function that is dependent on the number of deaths. Theoretical analyses show that the functional forms of the effective contact rate have no effect on initial disease transmission. Time-dependent controls for treatment and vaccination with a constant effective contact rate are incorporated to determine optimal control strategies. Numerical simulations show the short-term impact of media coverage on mitigating the spread of the disease, and it is observed that with three incidence functions used, the qualitative nature of the controls remains the same. The effective contact rates are graphically shown to have a population-level effect on the disease dynamics as the number of treated and recovered individuals could be significantly different. Finally, it is shown that treatment of infectives should be at its maximum rate for a longer period compared to vaccination, while concurrent implementation of vaccination and treatment is more impactful in mitigating the spread of the disease. Thus, it is imperative that media reports and health policy decision making on infectious diseases are contextualized.http://www.sciencedirect.com/science/article/pii/S2468227624000838Infectious diseaseMediaDifferential equationsBasic reproduction numberStability analysisOptimization |
| spellingShingle | Mamadou L. Diagne Folashade B. Agusto Herieth Rwezaura Jean M. Tchuenche Suzanne Lenhart Optimal control of an epidemic model with treatment in the presence of media coverage Scientific African Infectious disease Media Differential equations Basic reproduction number Stability analysis Optimization |
| title | Optimal control of an epidemic model with treatment in the presence of media coverage |
| title_full | Optimal control of an epidemic model with treatment in the presence of media coverage |
| title_fullStr | Optimal control of an epidemic model with treatment in the presence of media coverage |
| title_full_unstemmed | Optimal control of an epidemic model with treatment in the presence of media coverage |
| title_short | Optimal control of an epidemic model with treatment in the presence of media coverage |
| title_sort | optimal control of an epidemic model with treatment in the presence of media coverage |
| topic | Infectious disease Media Differential equations Basic reproduction number Stability analysis Optimization |
| url | http://www.sciencedirect.com/science/article/pii/S2468227624000838 |
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