Abdelhadi, Abta; Hassan, Laarabi Optimal control strategy for SEIR with latent period and a saturated incidence rate. (English) Zbl 1298.92092 ISRN Appl. Math. 2013, Article ID 706848, 4 p. (2013). Summary: We propose an SEIR epidemic model with latent period and a modified saturated incidence rate. This work investigates the fundamental role of the vaccination strategies to reduce the number of susceptible, exposed, and infected individuals and increase the number of recovered individuals. The existence of the optimal control of the nonlinear model is also proved. The optimality system is derived and then solved numerically using a competitive Gauss-Seidel-like implicit difference method. Cited in 1 Document MSC: 92D30 Epidemiology 93C95 Application models in control theory 34K20 Stability theory of functional-differential equations PDFBibTeX XMLCite \textit{A. Abdelhadi} and \textit{L. Hassan}, ISRN Appl. Math. 2013, Article ID 706848, 4 p. (2013; Zbl 1298.92092) Full Text: DOI References: [1] Hethcote, H. W.; Stech, H. W.; van den Driessche, P.; Busenberg, S. N.; Cooke, K. L., Periodicity and stability in epidemic models: a survey, Differential Equations and Applications in Ecology, Epidemics, and Population Problems, 6582 (1981), New York, NY, USA: Academic Press, New York, NY, USA [2] Kaddar, A.; Abta, A.; Alaoui, H. T., A comparison of delayed SIR and SEIR epidemic models, Nonlinear Analysis: Modelling and Control, 16, 2, 181-190 (2011) · Zbl 1322.92073 [3] Abta, A.; Kaddar, A.; Alaoui, H. T., Global stability for delay SIR and SEIR epidemic models with saturated incidence rates, Electronic Journal of Differential Equations, 2012, 23, 1-13 (2012) · Zbl 1243.34115 [4] Lukes, D. L., Differential Equations: Classical to Controlled. Differential Equations: Classical to Controlled, Mathematics in Science and Engineering, 162 (1982), New York, NY, USA: Academic Press, New York, NY, USA · Zbl 0509.34003 [5] Fleming, W. H.; Rishel, R. W., Deterministic and Stochastic Optimal Control (1975), New York, NY, USA: Springer, New York, NY, USA · Zbl 0323.49001 [6] Morton, I. K.; Nancy, L. S., Dynamics Optimization the Calculus of Variations and Optimal Control in Economics and Management (2000), Amsterdam, The Netherlands: Elsevier Science, Amsterdam, The Netherlands [7] Gumel, A. B.; Shivakumar, P. N.; Sahai, B. M., A mathematical model for the dynamics of HIV-1 during the typical course of infection, Proceedings of the 3rd World Congress of Nonlinear Analysts · Zbl 1042.92512 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.