Optimal control for SIRC epidemic outbreak

• Published in: Computer methods and programs in biomedicine Vol. 110; no. 3; pp. 333 - 342
• Main Authors: Iacoviello, Daniela, Stasio, Nicolino
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ireland Ltd 01.06.2013; Elsevier
• Subjects: Biological and medical sciences; Communicable Diseases - epidemiology; Communicable Diseases - immunology; Communicable Diseases - transmission; Computer Simulation; Epidemic models; Epidemics - prevention & control; Epidemics - statistics & numerical data; Epidemiology; Fundamental and applied biological sciences. Psychology; General aspects; Humans; Incidence; Infection Control; Internal Medicine; Mathematical Concepts; Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Medical sciences; Models, Biological; Optimal control; Optimization; Other; Public health. Hygiene; Public health. Hygiene-occupational medicine; SIRC model; System analysis; Epidemic models; SIRC model; System analysis; Optimal control; Optimization; Epidemic; Costs; Disease; Existence of solution; Vaccination; Pontryagin principle; Quarantine; Biomathematics; Epidemiology; Modeling; Optimal strategy; Minimum principle; Public health
• ISSN: 0169-2607; 1872-7565; 1872-7565
• DOI: 10.1016/j.cmpb.2013.01.006

In this paper the mathematical SIRC epidemic model is considered. It efficiently describes diseases in which a cross immune class (C) is present, along with the susceptible (S), the infected (I) and the removed (R) ones. Controlling epidemic diseases corresponds to the introduction of vaccination, quarantine and treatment strategies; generally only one of these actions is considered. In this paper the possibility of optimal controls both over the susceptible and the infected subjects is assumed, taking into account also limitations of resources. A suitable cost index is introduced and via the Pontryagin's Minimum Principle the optimal control strategy is determined and the existence of the optimal solution is assessed. Numerical results are developed analyzing the effects of different control strategies.