Optimal control of deterministic epidemics

被引:191
作者
Behncke, H [1 ]
机构
[1] Univ Osnabruck, FB Math Informat, D-49069 Osnabruck, Germany
关键词
optimal control; deterministic epidemics; infinite time-horizon problems; preventative health control;
D O I
10.1002/oca.678
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Various deterministic optimal control models for SIR-epidemics are investigated in this paper. The epidemics are governed by a rather general interaction, which covers most cases studied in the literature. Vaccination, quarantine, screening or health promotion campaigns as Forms of control are considered. In all cases one finds a maximum effort control on some initial time interval. In addition, uniqueness and monotonicity properties of these models are studied. The results are also extended to the infinite time-horizon situation. Copyright (C) 2000 John Wiley & Sons, Ltd.
引用
收藏
页码:269 / 285
页数:17
相关论文
共 13 条
[1]   EXISTENCE THEOREMS FOR LAGRANGE CONTROL PROBLEMS WITH UNBOUNDED TIME DOMAIN [J].
BAUM, RF .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1976, 19 (01) :89-116
[2]  
BRAUER F, 1990, J MATH BIOL, V28, P451
[3]   SOME CHARACTERIZATIONS OF OPTIMAL TRAJECTORIES IN CONTROL-THEORY [J].
CANNARSA, P ;
FRANKOWSKA, H .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1991, 29 (06) :1322-1347
[4]  
Filippov A., 1962, Journal of the Society for Industrial and Applied Mathematics, Series A: Control, V1, P76, DOI 10.1137/0301006
[5]   A SURVEY OF THE MAXIMUM-PRINCIPLES FOR OPTIMAL-CONTROL PROBLEMS WITH STATE CONSTRAINTS [J].
HARTL, RF ;
SETHI, SP ;
VICKSON, RG .
SIAM REVIEW, 1995, 37 (02) :181-218
[6]  
Hethcote H.W., 1973, Mathematical Biosci, V18, P365, DOI 10.1016/0025-5564(73)90011-4
[7]   SOME EPIDEMIOLOGIC MODELS WITH NONLINEAR INCIDENCE [J].
HETHCOTE, HW ;
VANDENDRIESSCHE, P .
JOURNAL OF MATHEMATICAL BIOLOGY, 1991, 29 (03) :271-287
[8]  
Morton R., 1974, Advances in Applied Probability, V6, P622, DOI 10.2307/1426183
[9]   DYNAMIC OPTIMAL-CONTROL MODELS IN ADVERTISING - SURVEY [J].
SETHI, SP .
SIAM REVIEW, 1977, 19 (04) :685-725
[10]   OPTIMAL CONTROL OF CARRIER-BORNE EPIDEMICS [J].
WICKWIRE, K .
JOURNAL OF APPLIED PROBABILITY, 1975, 12 (03) :565-568