Mathematical Modelling and optimal control of pneumonia disease in sheep and goats in Al-Baha region with cost-effective strategies
In this work, the concept of the fractional derivative is used to improve a mathematical model for the transmission dynamics of pneumonia in the Al-Baha region of the Kingdom of Saudi Arabia. We establish a dynamics model to predict the transmission of pneumonia in some local sheep and goat herds. T...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-04-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022669?viewType=HTML |
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| author | Sayed Saber Azza M. Alghamdi Ghada A. Ahmed Khulud M. Alshehri |
| author_facet | Sayed Saber Azza M. Alghamdi Ghada A. Ahmed Khulud M. Alshehri |
| author_sort | Sayed Saber |
| collection | DOAJ |
| description | In this work, the concept of the fractional derivative is used to improve a mathematical model for the transmission dynamics of pneumonia in the Al-Baha region of the Kingdom of Saudi Arabia. We establish a dynamics model to predict the transmission of pneumonia in some local sheep and goat herds. The proposed model is a generalization of a system of five ordinary differential equations of the first order, regarding five unknowns, which are the numbers of certain groups of animals (susceptible, vaccinated, carrier, infected, and recovered). This consists of investigating the equilibrium, basic reproduction number, stability analysis, and bifurcation analysis. It is observed that the free equilibrium point is local and global asymptotic stable if the basic reproduction number is less than one, and the endemic equilibrium is local and global asymptotic stable if the basic reproduction number is greater than one. The optimal control problem is formulated using Pontryagin's maximum principle, with three control strategies: Disease prevention through education, treatment, and screening. The most cost-effective intervention strategy to combat the pneumonia pandemic is a combination of prevention and treatment, according to the cost-effectiveness analysis of the adopted control techniques. A numerical simulation is performed, and the significant data are graphically displayed. The results predicted by the model show a good agreement with the actual reported data. |
| first_indexed | 2024-04-13T09:40:38Z |
| format | Article |
| id | doaj.art-09e8756182e246f09f1662958c778a99 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-13T09:40:38Z |
| publishDate | 2022-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-09e8756182e246f09f1662958c778a992022-12-22T02:51:56ZengAIMS PressAIMS Mathematics2473-69882022-04-0177120111204910.3934/math.2022669Mathematical Modelling and optimal control of pneumonia disease in sheep and goats in Al-Baha region with cost-effective strategiesSayed Saber 0Azza M. Alghamdi 1Ghada A. Ahmed2Khulud M. Alshehri31. Department of Mathematics, Al-Baha University, Baljurashi, Saudi Arabia 2. Department of Mathematics and Statistics, Faculty of Science, Beni-Suef University, Egypt3. Mathematics Department, Faculty of science, AL-Baha University, Saudi Arabia3. Mathematics Department, Faculty of science, AL-Baha University, Saudi Arabia4. Department of Biology, Al-Baha University, Baljurashi, Saudi ArabiaIn this work, the concept of the fractional derivative is used to improve a mathematical model for the transmission dynamics of pneumonia in the Al-Baha region of the Kingdom of Saudi Arabia. We establish a dynamics model to predict the transmission of pneumonia in some local sheep and goat herds. The proposed model is a generalization of a system of five ordinary differential equations of the first order, regarding five unknowns, which are the numbers of certain groups of animals (susceptible, vaccinated, carrier, infected, and recovered). This consists of investigating the equilibrium, basic reproduction number, stability analysis, and bifurcation analysis. It is observed that the free equilibrium point is local and global asymptotic stable if the basic reproduction number is less than one, and the endemic equilibrium is local and global asymptotic stable if the basic reproduction number is greater than one. The optimal control problem is formulated using Pontryagin's maximum principle, with three control strategies: Disease prevention through education, treatment, and screening. The most cost-effective intervention strategy to combat the pneumonia pandemic is a combination of prevention and treatment, according to the cost-effectiveness analysis of the adopted control techniques. A numerical simulation is performed, and the significant data are graphically displayed. The results predicted by the model show a good agreement with the actual reported data.https://www.aimspress.com/article/doi/10.3934/math.2022669?viewType=HTMLpneumonia modelstability analysisoptimal controlcost-effectiveness analysiscaputo fractional derivativefixed point theoremnumerical simulation |
| spellingShingle | Sayed Saber Azza M. Alghamdi Ghada A. Ahmed Khulud M. Alshehri Mathematical Modelling and optimal control of pneumonia disease in sheep and goats in Al-Baha region with cost-effective strategies AIMS Mathematics pneumonia model stability analysis optimal control cost-effectiveness analysis caputo fractional derivative fixed point theorem numerical simulation |
| title | Mathematical Modelling and optimal control of pneumonia disease in sheep and goats in Al-Baha region with cost-effective strategies |
| title_full | Mathematical Modelling and optimal control of pneumonia disease in sheep and goats in Al-Baha region with cost-effective strategies |
| title_fullStr | Mathematical Modelling and optimal control of pneumonia disease in sheep and goats in Al-Baha region with cost-effective strategies |
| title_full_unstemmed | Mathematical Modelling and optimal control of pneumonia disease in sheep and goats in Al-Baha region with cost-effective strategies |
| title_short | Mathematical Modelling and optimal control of pneumonia disease in sheep and goats in Al-Baha region with cost-effective strategies |
| title_sort | mathematical modelling and optimal control of pneumonia disease in sheep and goats in al baha region with cost effective strategies |
| topic | pneumonia model stability analysis optimal control cost-effectiveness analysis caputo fractional derivative fixed point theorem numerical simulation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022669?viewType=HTML |
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