Optimal control for an age-structured model for the transmission of hepatitis B
One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formul...
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| Published in | Journal of mathematical biology Vol. 73; no. 2; pp. 305 - 333 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.08.2016
Springer Nature B.V Springer |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0303-6812 1432-1416 1432-1416 |
| DOI | 10.1007/s00285-015-0952-6 |
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| Abstract | One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention. |
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| AbstractList | One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention.One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention. One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention. |
| Author | Tewa, Jean-Jules Emvudu, Yves Djidjou Demasse, Ramses Bowong, Samuel |
| Author_xml | – sequence: 1 givenname: Ramses surname: Djidjou Demasse fullname: Djidjou Demasse, Ramses email: ddramses@gmail.com organization: Faculty of Science, University of Yaounde 1, UMI 209 IRD&UPMC UMMISCO, LIRIMA, Project Team GRIMCAPE, The African Center of Excellence in Information and Communication Technologies (CETIC), University of Yaounde 1 – sequence: 2 givenname: Jean-Jules surname: Tewa fullname: Tewa, Jean-Jules organization: National Advanced School of Engineering, University of Yaounde 1, UMI 209 IRD&UPMC UMMISCO, LIRIMA, Project Team GRIMCAPE, The African Center of Excellence in Information and Communication Technologies (CETIC), University of Yaounde 1 – sequence: 3 givenname: Samuel surname: Bowong fullname: Bowong, Samuel organization: Faculty of Science, University of Douala, UMI 209 IRD&UPMC UMMISCO, LIRIMA, Project Team GRIMCAPE, The African Center of Excellence in Information and Communication Technologies (CETIC), University of Yaounde 1 – sequence: 4 givenname: Yves surname: Emvudu fullname: Emvudu, Yves organization: Faculty of Science, University of Yaounde 1 |
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| Keywords | 92D30 Stability 49J20 35B35 Age structure Optimal control Non-linear dynamical system HBV 35Q92 |
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