OPTIMAL CONTROL OF AN EPIDEMIC THROUGH EDUCATIONAL CAMPAIGNS

In this work we study the best strategy for educational campaigns during the outbreak of an epidemic. Assuming that the epidemic is described by the simplified SIR model and that the total time of the campaign is limited due to budget, we consider two possible scenarios. In the first scenario we have a campaign oriented to decrease the infection rate by stimulating susceptibles to have a protective behavior. In the second scenario we have a campaign oriented to increase the removal rate by stimulating the infected to remove themselves from the infected class. The optimality is taken to be to minimize the total number of infected by the end of the epidemic outbreak. The technical tool used to determine the optimal strategy is the Pontryagin Maximum Principle.

[1]  Herbert W. Hethcote,et al.  Optimal vaccination schedules in a deterministic epidemic model , 1973 .

[2]  K. Wickwire.  Mathematical models for the control of pests and infectious diseases: a survey. , 1977, Theoretical population biology.

[3]  J. Radcliffe,et al.  The Mathematical Theory of Infectious Diseases and its Applications , 1977 .

[4]  H. Behncke.  Optimal control of deterministic epidemics , 2000 .

[5]  A. Agrachev,et al.  Control Theory from the Geometric Viewpoint , 2004 .

[6]  Horst R. Thieme,et al.  Mathematics in Population Biology , 2003 .

[7]  R. E. Rink,et al.  Optimum control of epidemics , 1973 .

[8]  F. Brauer,et al.  Mathematical Models in Population Biology and Epidemiology , 2001 .

[9]  J. Ball.  OPTIMIZATION—THEORY AND APPLICATIONS Problems with Ordinary Differential Equations (Applications of Mathematics, 17) , 1984 .

[10]  M. L. Chambers.  The Mathematical Theory of Optimal Processes , 1965 .

[11]  V. Jurdjevic.  Geometric control theory , 1996 .

[12]  Urszula Ledzewicz,et al.  Optimal Bang-Bang Controls for a Two-Compartment Model in Cancer Chemotherapy , 2002 .

[13]  Klaus Dietz,et al.  Mathematical Models for Infectious Disease Statistics , 1985 .

[14]  L. Bobisud.  Optimal control of a deterministic epidemic , 1977 .

[15]  Philippe Souères,et al.  Optimal trajectories for nonholonomic mobile robots , 1998 .

[16]  G S Zaric,et al.  Resource allocation for epidemic control over short time horizons. , 2001, Mathematical biosciences.