TY - JOUR
T1 - Global analysis and optimal control of a periodic visceral leishmaniasis model
AU - ELmojtaba, Ibrahim M.
AU - Biswas, Santanu
AU - Chattopadhyay, Joydev
N1 - Publisher Copyright:
© 2017 by the author.
PY - 2017/12/14
Y1 - 2017/12/14
N2 - 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 R0, the basic reproduction number, is less than unity. When R0 > 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.
AB - 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 R0, the basic reproduction number, is less than unity. When R0 > 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.
KW - Global stability analysis
KW - Non-autonomous system
KW - Optimal control
KW - Periodic solutions
KW - Visceral leishmaniasis
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U2 - 10.3390/math5040080
DO - 10.3390/math5040080
M3 - Article
AN - SCOPUS:85038240413
SN - 2227-7390
VL - 5
JO - Mathematics
JF - Mathematics
IS - 4
M1 - 80
ER -