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Free Optimal Time Control Problem for a SEIR-Epidemic Model with Immigration of Infective

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2017
Mustapha Lhous, Mostafa Rachik, Abdelilah Larrache

Mustapha Lhous, Mostafa Rachik and Abdelilah Larrache. Free Optimal Time Control Problem for a SEIR-Epidemic Model with Immigration of Infective. International Journal of Computer Applications 159(3):1-5, February 2017. BibTeX

	author = {Mustapha Lhous and Mostafa Rachik and Abdelilah Larrache},
	title = {Free Optimal Time Control Problem for a SEIR-Epidemic Model with Immigration of Infective},
	journal = {International Journal of Computer Applications},
	issue_date = {February 2017},
	volume = {159},
	number = {3},
	month = {Feb},
	year = {2017},
	issn = {0975-8887},
	pages = {1-5},
	numpages = {5},
	url = {},
	doi = {10.5120/ijca2017912886},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


In the present paper, we consider a mathematical model of a SEIR with immigration of infectives. The optimal control theory is applied to reduce the latent and infectious groups, increase the number of recovered individuals and this with an optimal cost. We use two controls representing the effort that reduces the contact between the infectious and susceptible individuals and a therapeutic treatment. We presents an approach that investigates a free terminal optimal time control witch give a minimum duration of a vaccination campaign. The Pontryagin’s maximum principle is used to characterize the optimal controls and the optimal final time.We obtained an optimality system that we sought to solve numerically by an iterative discrete scheme that converges following an appropriate test similar the one related to the forward-backward sweep method.


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SEIR-Epidemic model, Optimal control, Vaccination, Immigration