Next Article in Journal
Multiplicative Structure and Hecke Rings of Generator Matrices for Codes over Quotient Rings of Euclidean Domains
Previous Article in Journal
Hyperfuzzy Ideals in BCK/BCI-Algebras
Open AccessArticle

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
Show Figures

Figure 1

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop