Global Analysis and Optimal Control of a Periodic Visceral Leishmaniasis Model

被引：1
|
作者：
ELmojtaba, Ibrahim M. [1 ]
Biswas, Santanu [2 ]
Chattopadhyay, Joydev [2 ]
机构：
[1] Sultan Qaboos Univ, Coll Sci, Dept Math & Stat, Muscat 123, Oman
[2] Indian Stat Inst, Agr & Ecol Res Unit, 203 BT Rd, Kolkata 700108, India
来源：
MATHEMATICS | 2017年 / 5卷 / 04期
关键词：
visceral leishmaniasis; non-autonomous system; periodic solutions; global stability analysis; optimal control; TRANSMISSION; DYNAMICS;
D O I：
10.3390/math5040080
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 omega-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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页数：18
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