Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model

Ibrahim M. ELmojtaba, Santanu Biswas and Joydev Chattopadhyay
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Ibrahim M. ELmojtaba: Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, Muscat 123, Oman
Santanu Biswas: Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India
Joydev Chattopadhyay: Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India

Mathematics, 2017, vol. 5, issue 4, 1-18

Abstract: 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 ? -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.

Keywords: visceral leishmaniasis; non-autonomous system; periodic solutions; global stability analysis; optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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