OPTIMAL CONTROL OF THE TRANSMISSION RATE IN COMPARTMENTAL EPIDEMICS

被引:12
|
作者
Freddi, Lorenzo [1 ]
机构
[1] Univ Udine, Dipt Sci Matemat Informatiche Fis DMIF, Via Sci 206, I-33100 Udine, Italy
关键词
Optimal control; calculus of variations; compartmental epidemics; VACCINATION; STRATEGIES; MODEL;
D O I
10.3934/mcrf.2021007
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce a general system of ordinary differential equations that includes some classical and recent models for the epidemic spread in a closed population without vital dynamic in a finite time horizon. The model is vectorial, in the sense that it accounts for a vector valued state function whose components represent various kinds of exposed/infected subpopulations, with a corresponding vector of control functions possibly different for any subpop-ulation. In the general setting, we prove well-posedness and positivity of the initial value problem for the system of state equations and the existence of solutions to the optimal control problem of the coefficients of the nonlinear part of the system, under a very general cost functional. We also prove the uniqueness of the optimal solution for a small time horizon when the cost is superlinear in all control variables with possibly different exponents in the in-terval (1, 2]. We consider then a linear cost in the control variables and study the singular arcs. Full details are given in the case n = 1 and the results are illustrated by the aid of some numerical simulations.
引用
收藏
页码:201 / 223
页数:23
相关论文
共 50 条
  • [1] Transmission dynamics and optimal control of measles epidemics
    Pang, Liuyong
    Ruan, Shigui
    Liu, Sanhong
    Zhao, Zhong
    Zhang, Xinan
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 256 : 131 - 147
  • [2] Optimal control of deterministic epidemics
    Behncke, H
    OPTIMAL CONTROL APPLICATIONS & METHODS, 2000, 21 (06): : 269 - 285
  • [3] Optimal control of epidemics in metapopulations
    Rowthorn, Robert E.
    Laxminarayan, Ramanan
    Gilligan, Christopher A.
    JOURNAL OF THE ROYAL SOCIETY INTERFACE, 2009, 6 (41) : 1135 - 1144
  • [4] Modeling Epidemics With Compartmental Models
    Tolles, Juliana
    ThaiBinh Luong
    JAMA-JOURNAL OF THE AMERICAN MEDICAL ASSOCIATION, 2020, 323 (24): : 2515 - 2516
  • [5] Optimal control of epidemics with limited resources
    Elsa Hansen
    Troy Day
    Journal of Mathematical Biology, 2011, 62 : 423 - 451
  • [6] Optimal control of epidemics with limited resources
    Hansen, Elsa
    Day, Troy
    JOURNAL OF MATHEMATICAL BIOLOGY, 2011, 62 (03) : 423 - 451
  • [7] Optimal and sub-optimal control in Dengue epidemics
    Caetano, MAL
    Yoneyama, T
    OPTIMAL CONTROL APPLICATIONS & METHODS, 2001, 22 (02): : 63 - 73
  • [8] Optimal control of compartmental models: The exact solution
    Blanchini, Franco
    Bolzern, Paolo
    Colaneri, Patrizio
    De Nicolao, Giuseppe
    Giordano, Giulia
    AUTOMATICA, 2023, 147
  • [9] An autonomous compartmental model for accelerating epidemics
    Budanur, Nazmi Burak
    Hof, Bjorn
    PLOS ONE, 2022, 17 (07):
  • [10] A compartmental model for cyber-epidemics
    Aleja, D.
    Contreras-Aso, G.
    Alfaro-Bittner, K.
    Primo, E.
    Criado, R.
    Romance, M.
    Boccaletti, S.
    CHAOS SOLITONS & FRACTALS, 2022, 161