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Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model

1
Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Muscat 123, Oman
2
Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India
*
Author to whom correspondence should be addressed.
Mathematics 2017, 5(4), 80; https://doi.org/10.3390/math5040080
Received: 2 October 2017 / Revised: 6 November 2017 / Accepted: 12 November 2017 / Published: 14 December 2017
In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R 0 , the basic reproduction number, is less than unity. When R 0 > 1 and under some conditions, then our system has a unique positive ω -periodic solution that is globally asymptotically stable. Applying two controls, vaccination and treatment, to our model forces the system to be non-periodic, and all fractions of infected populations settle on a very low level. View Full-Text
Keywords: visceral leishmaniasis; non-autonomous system; periodic solutions; global stability analysis; optimal control visceral leishmaniasis; non-autonomous system; periodic solutions; global stability analysis; optimal control
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MDPI and ACS Style

ELmojtaba, I.M.; Biswas, S.; Chattopadhyay, J. Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model. Mathematics 2017, 5, 80. https://doi.org/10.3390/math5040080

AMA Style

ELmojtaba IM, Biswas S, Chattopadhyay J. Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model. Mathematics. 2017; 5(4):80. https://doi.org/10.3390/math5040080

Chicago/Turabian Style

ELmojtaba, Ibrahim M.; Biswas, Santanu; Chattopadhyay, Joydev. 2017. "Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model" Mathematics 5, no. 4: 80. https://doi.org/10.3390/math5040080

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