Optimal and sub-optimal quarantine and isolation control in SARS epidemics

Abstract

This paper discusses the application of optimal and sub-optimal controls to a SEQIJR SARS model via the Pontryagin's Maximum Principle. To this end, two control variables representing the quarantine and isolation strategies are considered in the model. The numerical optimal control laws are implemented in an iterative method, and the sub-optimal solution is computed using a genetic algorithm. The simulation results demonstrate that the maximal applications of quarantining and isolation strategies in the early stage of the epidemic are of very critical impacts in both cases of optimal and sub-optimal control. Otherwise, the control effect will be much worse. This gives a theoretical interpretation to the practical experiences that the early quarantine and isolation strategies are critically important to control the outbreaks of epidemics. Furthermore, our results also show that the proposed suboptimal control can lead to performances close to the optimal control, but with much simpler strategies for long periods of time in practical use.

Optimal control in epidemiology

“…Optimal control has been used, in the past, to find an optimal schedule for vaccine, treatment and chemotherapy for an infected individual. It has also been used to optimally manage the resources associated to quarantine and isolation programs Yan and Zou (2008).…”

“…Since economic resources are limited, epidemiological models have started taking into consideration the economic constraints imposed by limited resources when analyzing control strategies. Optimal control theory has been applied to the mathematical models of HIV models Zarei et al (2010), Kwon et al (2012), Karrakchou et al (2006), Kwon (2007), Roshanfekr et al (2014), , Zhou et al (2014), Adams et al (2005), Costanza et al (2013), Orellana (2011), Malaria Okosun et al (2013, Okosun et al (2011), Okosun and Makinde (2014), Okosun (2011), Kim (2012), Prosper et al (2014), Tuberculosis Moualeu et al (2015), Silva and Torres (2013), Agusto and Adekunle (2014), Bowong and Aziz Alaoui (2013), Whang et al (2011), Vector borne diseases Lashari (2012), Graesboll et al (2014), Sung Lee and Ali Lashari (2014) and other diseases Yan and Zou (2008), Agusto (2013), Brown andJane White (2011), Zaman et al (2008), Okosun and Makinde (2014), Su and Sun (2015), Buonomo et al (2014), Lowden et al (2014), Roshanfekr et al (2014), Apreutesei et al (2014), Imran et al (2014).…”

Optimal Control and Sensitivity Analysis of an Influenza Model with Treatment and Vaccination

“…More often the cost of implementing a control would be nonlinear. In this paper, a quadratic function is implemented for measuring the control cost (Blayneh et al 2009;Caetano and Yoneyama 2001;Felippe De Souza et al 2000;Joshi 2002;Karrakchou et al 2006;Kirschner et al 1997;Lenhart and Bhat 1992;Lenhart and Yong 1997;Yan et al 2007;Yan and Zou 2008). Furthermore, A 2 S(t f ), A 3 V(t f ) are respectively the fitness of the susceptible and the vaccinated group at the end of the process as a result of a reduction in the rate at which vaccine wanes, vaccinated and treatment efforts are implemented.…”

Non-Fragile Robust Guaranteed Cost Control of 2-D Discrete Uncertain Systems Described by the General Models

“…Equation (4) is the performance function of system (Σ). In the 1-D case, a quadratic function is implemented for measuring the control cost by reference to many papers in control [36]. When a system is 2-D, we need consider a 2-D quadratic cost function, which also means a generalized energy of the two-indexed motion variables.…”