Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System
We consider a discrete-time susceptible-infected-removed-susceptible “again” (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible population. In addition, we define a new compartment, which mo...
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| Vydané v: | Mathematical and computational applications Ročník 23; číslo 4; s. 52 |
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01.12.2018
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| Abstract | We consider a discrete-time susceptible-infected-removed-susceptible “again” (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible population. In addition, we define a new compartment, which models the dynamics of the number of controlled individuals and who are supposed not to be able to reach a long-term immunity due to the limited effect of control. Furthermore, we treat the resolution of this optimal control problem when there is a restriction on the number of susceptible people who have been controlled along the time of the control strategy. Further, we provide sufficient and necessary conditions for the existence of the sought optimal control, whose characterization is also given in accordance with an isoperimetric constraint. Finally, we present the numerical results obtained, using a computational method, which combines the secant method with discrete progressive-regressive schemes for the resolution of the discrete two-point boundary value problem. |
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| AbstractList | We consider a discrete-time susceptible-infected-removed-susceptible "again" (SIRS) epidemic model, and we introduce an optimal control function to seek the best control policy for preventing the spread of an infection to the susceptible population. In addition, we define a new compartment, which models the dynamics of the number of controlled individuals and who are supposed not to be able to reach a long-term immunity due to the limited effect of control. Furthermore, we treat the resolution of this optimal control problem when there is a restriction on the number of susceptible people who have been controlled along the time of the control strategy. Further, we provide sufficient and necessary conditions for the existence of the sought optimal control, whose characterization is also given in accordance with an isoperimetric constraint. Finally, we present the numerical results obtained, using a computational method, which combines the secant method with discrete progressive-regressive schemes for the resolution of the discrete two-point boundary value problem. |
| Author | Abouelkheir, Imane Rachik, Mostafa Elmouki, Ilias El Kihal, Fadwa |
| Author_xml | – sequence: 1 givenname: Fadwa orcidid: 0000-0003-3089-1150 surname: El Kihal fullname: El Kihal, Fadwa – sequence: 2 givenname: Imane surname: Abouelkheir fullname: Abouelkheir, Imane – sequence: 3 givenname: Mostafa surname: Rachik fullname: Rachik, Mostafa – sequence: 4 givenname: Ilias orcidid: 0000-0002-4826-5601 surname: Elmouki fullname: Elmouki, Ilias |
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| Cites_doi | 10.1201/9781420011418 10.1016/j.protcy.2014.10.249 10.1007/s40435-016-0233-2 10.1016/j.na.2007.08.036 10.1090/dimacs/075/03 10.1007/s10479-015-1834-4 10.3934/mbe.2006.3.557 10.1016/j.mbs.2013.10.006 10.1137/040604947 10.1186/s13662-016-0900-9 10.1007/s40819-017-0337-1 10.1155/S0161171294000487 10.9734/BJMCS/2017/31355 10.1186/s13662-015-0549-9 10.1016/j.nonrwa.2009.04.007 10.1007/s11766-004-0027-8 10.1016/j.mbs.2015.11.004 10.1016/j.cnsns.2018.01.011 10.1016/j.cnsns.2016.08.005 10.1007/s40435-014-0106-5 10.1016/j.jtbi.2007.10.014 10.1016/j.chaos.2007.07.047 10.1186/s13662-017-1168-4 10.1007/978-3-319-10380-8_14 10.1016/j.chaos.2006.04.022 10.1016/j.nonrwa.2011.12.024 10.1016/j.nonrwa.2011.07.036 |
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| Title | Optimal Control and Computational Method for the Resolution of Isoperimetric Problem in a Discrete-Time SIRS System |
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