Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model
Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Muscat 123, Oman
Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India
Author to whom correspondence should be addressed.
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
, the basic reproduction number, is less than unity. When
and under some conditions, then our system has a unique positive
-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.
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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.
ELmojtaba IM, Biswas S, Chattopadhyay J. Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model. Mathematics. 2017; 5(4):80.
ELmojtaba, Ibrahim M.; Biswas, Santanu; Chattopadhyay, Joydev. 2017. "Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model." Mathematics 5, no. 4: 80.
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