Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) Disease
In this paper, a model for the transmission of respiratory syncytial virus (RSV) in a constant human population in which there exist super spreading infected individuals (who infect many people during a single encounter) is considered. It has been observed in the epidemiological data for the disease...
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MDPI AG
2022-07-01
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| Online Access: | https://www.mdpi.com/2079-3197/10/7/120 |
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| author | Rattiya Sungchasit I-Ming Tang Puntani Pongsumpun |
| author_facet | Rattiya Sungchasit I-Ming Tang Puntani Pongsumpun |
| author_sort | Rattiya Sungchasit |
| collection | DOAJ |
| description | In this paper, a model for the transmission of respiratory syncytial virus (RSV) in a constant human population in which there exist super spreading infected individuals (who infect many people during a single encounter) is considered. It has been observed in the epidemiological data for the diseases caused by this virus that there are cases where some individuals are super-spreaders of the virus. We formulate a simply SEI<sub>r</sub>I<sub>s</sub>R (susceptible–exposed–regular infected–super-spreading infected–recovered) mathematical model to describe the dynamics of the transmission of this disease. The proposed model is analyzed using the standard stability method by using Routh-Hurwitz criteria. We obtain the basic reproductive number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>) using the next generation method. We establish that when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, the disease-free state is locally asymptotically stable and the disease endemic state is unstable. The reverse is true when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, the disease endemic state becomes the locally asymptotically stable state and the disease-free state becomes unstable. It is also established that the two equilibrium states are globally asymptotically stable. The numerical simulations show how the dynamics of the disease change as values of the parameters in the SEI<sub>r</sub>I<sub>s</sub>R are varied. |
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| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-09T10:20:05Z |
| publishDate | 2022-07-01 |
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| record_format | Article |
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| spelling | doaj.art-33083837961440c7906ef17b356034f02023-12-01T22:02:10ZengMDPI AGComputation2079-31972022-07-0110712010.3390/computation10070120Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) DiseaseRattiya Sungchasit0I-Ming Tang1Puntani Pongsumpun2Department of Mathematics, Faculty of Science, Phuket Rajabhat University, Phuket 83000, ThailandDepartment of Physics, Faculty of Science, Mahidol University, Bangkok 10400, ThailandDepartment of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, ThailandIn this paper, a model for the transmission of respiratory syncytial virus (RSV) in a constant human population in which there exist super spreading infected individuals (who infect many people during a single encounter) is considered. It has been observed in the epidemiological data for the diseases caused by this virus that there are cases where some individuals are super-spreaders of the virus. We formulate a simply SEI<sub>r</sub>I<sub>s</sub>R (susceptible–exposed–regular infected–super-spreading infected–recovered) mathematical model to describe the dynamics of the transmission of this disease. The proposed model is analyzed using the standard stability method by using Routh-Hurwitz criteria. We obtain the basic reproductive number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>) using the next generation method. We establish that when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, the disease-free state is locally asymptotically stable and the disease endemic state is unstable. The reverse is true when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, the disease endemic state becomes the locally asymptotically stable state and the disease-free state becomes unstable. It is also established that the two equilibrium states are globally asymptotically stable. The numerical simulations show how the dynamics of the disease change as values of the parameters in the SEI<sub>r</sub>I<sub>s</sub>R are varied.https://www.mdpi.com/2079-3197/10/7/120global dynamical modeling methodLyapunov function methodnext generation matrixrespiratory syncytial virus (RSV)basic reproduction number |
| spellingShingle | Rattiya Sungchasit I-Ming Tang Puntani Pongsumpun Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) Disease Computation global dynamical modeling method Lyapunov function method next generation matrix respiratory syncytial virus (RSV) basic reproduction number |
| title | Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) Disease |
| title_full | Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) Disease |
| title_fullStr | Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) Disease |
| title_full_unstemmed | Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) Disease |
| title_short | Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) Disease |
| title_sort | mathematical modeling global stability analysis of super spreading transmission of respiratory syncytial virus rsv disease |
| topic | global dynamical modeling method Lyapunov function method next generation matrix respiratory syncytial virus (RSV) basic reproduction number |
| url | https://www.mdpi.com/2079-3197/10/7/120 |
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