Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate
Abstract Toxoplasma infection in humans is considered due to direct contact with infected cats. Toxoplasma infection (an endemic disease) has the potential to affect various organs and systems (brain, eyes, heart, lungs, liver, and lymph nodes). Bilinear incidence rate and constant population (birth...
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Nature Portfolio
2024-06-01
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| author | Usman Khan Farhad Ali Ohud A. Alqasem Maysaa E. A. Elwahab Ilyas Khan Ariana Abdul Rahimzai |
| author_facet | Usman Khan Farhad Ali Ohud A. Alqasem Maysaa E. A. Elwahab Ilyas Khan Ariana Abdul Rahimzai |
| author_sort | Usman Khan |
| collection | DOAJ |
| description | Abstract Toxoplasma infection in humans is considered due to direct contact with infected cats. Toxoplasma infection (an endemic disease) has the potential to affect various organs and systems (brain, eyes, heart, lungs, liver, and lymph nodes). Bilinear incidence rate and constant population (birth rate is equal to death rate) are used in the literature to explain the dynamics of Toxoplasmosis disease transmission in humans and cats. The goal of this study is to consider the mathematical model of Toxoplasma disease with harmonic mean type incident rate and also consider that the population of humans and cats is not equal (birth rate and the death rate are not equal). In examining Toxoplasma transmission dynamics in humans and cats, harmonic mean incidence rates are better than bilinear incidence rates. The disease dynamics are first schematically illustrated, and then the law of mass action is applied to obtain nonlinear ordinary differential equations (ODEs). Analysis of the boundedness, positivity, and equilibrium points of the system has been analyzed. The reproduction number is calculated using the next-generation matrix technique. The stability of disease-free and endemic equilibrium are analyzed. Sensitivity analysis is also done for reproduction number. Numerical simulation shows that the infection is spread in the population when the contact rate $$\beta_{h}$$ β h and $$\beta_{c}$$ β c increases while the infection is reduced when the recovery rate $$\delta_{h}$$ δ h increases. This study investigates the impact of various optimal control strategies, such as vaccinations for the control of disease and the awareness of disease awareness, on the management of disease. |
| format | Article |
| id | doaj-art-8b3f7144538542b680dc68d9d3c270ba |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-06-01 |
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| spelling | doaj-art-8b3f7144538542b680dc68d9d3c270ba2025-01-12T12:25:13ZengNature PortfolioScientific Reports2045-23222024-06-0114111810.1038/s41598-024-63263-wOptimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rateUsman Khan0Farhad Ali1Ohud A. Alqasem2Maysaa E. A. Elwahab3Ilyas Khan4Ariana Abdul Rahimzai5Department of Mathematics, City University of Science and Information TechnologyDepartment of Mathematics, City University of Science and Information TechnologyDepartment of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman UniversityDepartment of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman UniversityDepartment of Mathematics, College of Science Al-Zulfi, Majmaah UniversityDepartment of Mathematics, Education Faculty, Laghman UniversityAbstract Toxoplasma infection in humans is considered due to direct contact with infected cats. Toxoplasma infection (an endemic disease) has the potential to affect various organs and systems (brain, eyes, heart, lungs, liver, and lymph nodes). Bilinear incidence rate and constant population (birth rate is equal to death rate) are used in the literature to explain the dynamics of Toxoplasmosis disease transmission in humans and cats. The goal of this study is to consider the mathematical model of Toxoplasma disease with harmonic mean type incident rate and also consider that the population of humans and cats is not equal (birth rate and the death rate are not equal). In examining Toxoplasma transmission dynamics in humans and cats, harmonic mean incidence rates are better than bilinear incidence rates. The disease dynamics are first schematically illustrated, and then the law of mass action is applied to obtain nonlinear ordinary differential equations (ODEs). Analysis of the boundedness, positivity, and equilibrium points of the system has been analyzed. The reproduction number is calculated using the next-generation matrix technique. The stability of disease-free and endemic equilibrium are analyzed. Sensitivity analysis is also done for reproduction number. Numerical simulation shows that the infection is spread in the population when the contact rate $$\beta_{h}$$ β h and $$\beta_{c}$$ β c increases while the infection is reduced when the recovery rate $$\delta_{h}$$ δ h increases. This study investigates the impact of various optimal control strategies, such as vaccinations for the control of disease and the awareness of disease awareness, on the management of disease.https://doi.org/10.1038/s41598-024-63263-wToxoplasmosis transmissionDeterministic epidemic modelStability analysisNumerical simulationOptimal control |
| spellingShingle | Usman Khan Farhad Ali Ohud A. Alqasem Maysaa E. A. Elwahab Ilyas Khan Ariana Abdul Rahimzai Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate Scientific Reports Toxoplasmosis transmission Deterministic epidemic model Stability analysis Numerical simulation Optimal control |
| title | Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate |
| title_full | Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate |
| title_fullStr | Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate |
| title_full_unstemmed | Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate |
| title_short | Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate |
| title_sort | optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean type incident rate |
| topic | Toxoplasmosis transmission Deterministic epidemic model Stability analysis Numerical simulation Optimal control |
| url | https://doi.org/10.1038/s41598-024-63263-w |
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