Optimal control of normalized SIMR models with vaccination and treatment
| Autor: | Helmut Maurer, Maria do Rosário de Pinho, Hasnaa Zidani |
|---|---|
| Přispěvatelé: | Faculdade de Engenharia, SYSTEC, DEEC, Faculdade de Engenharia da Universidade do Porto, Institut für Numerische und Angewandte Mathematik, Westfälische Wilhelms-Universität Münster (WWU), Optimisation et commande (OC), Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris) |
| Rok vydání: | 2018 |
| Předmět: |
0209 industrial biotechnology
Mathematical optimization education.field_of_study 021103 operations research Computer science Applied Mathematics Direct method Population 0211 other engineering and technologies Order (ring theory) 02 engineering and technology Optimal control 3. Good health Model predictive control 020901 industrial engineering & automation Discrete Mathematics and Combinatorics [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Sensitivity (control systems) education Epidemic model ComputingMilieux_MISCELLANEOUS [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Hamiltonian (control theory) |
| Zdroj: | Discrete and Continuous Dynamical Systems-Series B Discrete and Continuous Dynamical Systems-Series B, American Institute of Mathematical Sciences, 2018, 23 (1), pp.79-99. ⟨10.3934/dcdsb.2018006⟩ Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 1553-524X 1531-3492 |
| DOI: | 10.3934/dcdsb.2018006 |
| Popis: | We study a model based on the so called SIR model to control the spreading of a disease in a varying population via vaccination and treatment. Since we assume that medical treatment is not immediate we add a new compartment, \begin{document}$M$\end{document} , to the SIR model. We work with the normalized version of the proposed model. For such model we consider the problem of steering the system to a specified target. We consider both a fixed time optimal control problem with \begin{document}$L^1$\end{document} cost and the minimum time problem to drive the system to the target. In contrast to the literature, we apply different techniques of optimal control to our problems of interest.Using the direct method, we first solve the fixed time problem and then proceed to validate the computed solutions using both necessary conditions and second order sufficient conditions. Noteworthy, we perform a sensitivity analysis of the solutions with respect to some parameters in the model. We also use the Hamiltonian Jacobi approach to study how the minimum time function varies with respect to perturbations of the initial conditions. Additionally, we consider a multi-objective approach to study the trade off between the minimum time and the social costs of the control of diseases. Finally, we propose the application of Model Predictive Control to deal with uncertainties of the model. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|