G. Chowell, P. Fenimore, M. Castillo-Garsow, and C. Castillo-Chavez, “SARS outbreaks in Ontario, Hong Kong and Singapore: The role of diagnosis and isolation as a control mechanism,” Journal of Theoretical Biology, vol. 224, no. 1, pp. 1-8, 2003.
 C. Nowzari, V. M. Preciado, and G. J. Pappas, “Optimal resource allocation for control of networked epidemic models,” IEEE Transactions on Control of Network Systems, vol. 4, no. 2, pp. 159-169, 2017.
 M. Pezzutto, N. B. Rossello, L. Schenato, and E. Garone, “Smart testing and selective quarantine for the control of epidemics,” arXiv:2007.15412, 2020.
 J. Ely, A. Galeotti, and J. Steiner, “Optimal test allocation,” Mimeo, Tech. Rep., 2020.
 F. Piguillem and L. Shi, “Optimal COVID-19 quarantine and testing policies,” CEPR Discussion Paper No. DP14613, 2020.
 D. Berger, K. Herkenhoff, and S. Mongey, “An SEIR infectious disease model with testing and conditional quarantine,” NBER Working Paper No. 26901, 2020. [OpenAIRE]
 A. Charpentier, R. Elie, M. Laurie´re, and V. Tran, “COVID-19 pandemic control: Balancing detection policy and lockdown intervention under ICU sustainability,” arXiv:2005.06526v3, 2020.
 G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, A. Di Matteo, and M. Colaneri, “Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy,” Nature medicine, vol. 26, pp. 855-860, June 2020.
 Z. Liu, P. Magal, O. Seydi, and G. Webb, “Understanding unreported cases in the COVID-19 epidemic outbreak in Wuhan, China, and the importance of major public health interventions,” Biology, vol. 9, no. 3, p. 50, 2020.
 A. Ducrot, P. Magal, T. Nguyen, and G. Webb, “Identifying the number of unreported cases in SIR epidemic models,” Mathematical medicine and biology: A journal of the IMA, vol. 37, no. 2, pp. 243-261, 2020.
Testing is a crucial control mechanism for an epidemic outbreak because it enables the health authority to detect and isolate the infected cases, thereby limiting the disease transmission to susceptible people, when no effective treatment or vaccine is available. In this paper, an epidemic model that incorporates the testing rate as a control input is presented. The proposed model distinguishes between the undetected infected and the detected infected cases with the latter assumed to be isolated from the disease spreading process in the population. Two testing policies, effective during the onset of an epidemic when no treatment or vaccine is available, are devised: (i) best-effort strategy for testing (BEST) and (ii) constant optimal strategy for testing (COST). The BEST is a suppression policy that provides a lower bound on the testing rate to stop the growth of the epidemic. The COST is a mitigation policy that minimizes the peak of the epidemic by providing a constant, optimal allocation of tests in a certain time interval when the total stockpile of tests is limited. Both testing policies are evaluated by their impact on the number of active intensive care unit (ICU) cases and the cumulative number of deaths due to COVID-19 in France.
Comment: arXiv admin note: substantial text overlap with arXiv:2010.15438