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.
引用
收藏
页数：18
相关论文
共 50 条
  • [31] Mathematical modeling of Visceral Leishmaniasis and control strategies
    Biswas, Santanu
    [J]. CHAOS SOLITONS & FRACTALS, 2017, 104 : 546 - 556
  • [32] Uniting mathematics and biology for control of visceral leishmaniasis
    Rock, Kat S.
    le Rutte, Epke A.
    de Vlas, Sake J.
    Adams, Emily R.
    Medley, Graham F.
    Hollingsworth, T. Deirdre
    [J]. TRENDS IN PARASITOLOGY, 2015, 31 (06) : 251 - 259
  • [33] The control of visceral leishmaniasis in Brazil: end of a cycle?
    Werneck, Guilherme L.
    [J]. CADERNOS DE SAUDE PUBLICA, 2016, 32 (06):
  • [34] Visceral leishmaniasis control: a public health perspective
    Boelaert, M
    Criel, B
    Leeuwenburg, J
    Van Damme, W
    Le Ray, D
    Van der Stuyft, P
    [J]. TRANSACTIONS OF THE ROYAL SOCIETY OF TROPICAL MEDICINE AND HYGIENE, 2000, 94 (05) : 465 - 471
  • [35] Prospects for visceral leishmaniasis control in Amazonian municipalities
    Garcez, Lourdes Maria
    Chagas, Anadeiva Portela
    Fonseca Gomes, Patrick Abdala
    Cardoso, Joyce Favacho
    Correia Miranda, Jefferson Francisco
    Jeronimo Dickson, Luis Antonio
    Mota, Eduardo Ferreira
    Bezerra, Lucilandia Maria
    Fraiha Neto, Habib
    Quinnell, Rupert Julian
    Courtenay, Orin
    [J]. REVISTA DA SOCIEDADE BRASILEIRA DE MEDICINA TROPICAL, 2008, 41 : 95 - 96
  • [36] Global stability analysis and optimal control of measles model with vaccination and treatment
    Ratchada Viriyapong
    Witchaya Ridbamroong
    [J]. Journal of Applied Mathematics and Computing, 2020, 62 : 207 - 237
  • [37] Global stability analysis and optimal control of measles model with vaccination and treatment
    Viriyapong, Ratchada
    Ridbamroong, Witchaya
    [J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2020, 62 (1-2) : 207 - 237
  • [38] AN EXPERIMENTAL-MODEL FOR CANINE VISCERAL LEISHMANIASIS
    ABRANCHES, P
    SANTOSGOMES, G
    RACHAMIM, N
    CAMPINO, L
    SCHNUR, LF
    JAFFE, CL
    [J]. PARASITE IMMUNOLOGY, 1991, 13 (05) : 537 - 550
  • [39] Vaccination model for visceral leishmaniasis with infective immigrants
    ELmojtaba, Ibrahim M.
    Mugisha, J. Y. T.
    Hashim, Andmohsin H. A.
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 36 (02) : 216 - 226
  • [40] Sex-structured disease transmission model and control mechanisms for visceral leishmaniasis (VL)
    Awoke, Temesgen Debas
    Kassa, Semu Mitiku
    Morupisi, Kgomotso Suzan
    Tsidu, Gizaw Mengistu
    [J]. PLOS ONE, 2024, 19 (04):
12345