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Mathematical modeling of Visceral Leishmaniasis and control strategies

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  • Biswas, Santanu

Abstract

In this article, the author studies the dynamics of Visceral Leishmaniasis disease to analyze the seasonal VL incidence data from South Sudan during the period January, 2011 to December, 2011. The seasonality is consolidated in the model as sandfly growing rate, which is presumed to be time periodic. The basic reproduction number (R0) has been derived and estimated. On the premise of statistical and epidemiological information of South Sudan, parameters in the model are estimated. The author discusses an optimal control strategy among the two preventive measures namely use of vaccination and possible treatment of infective humans. Numerical findings indicate that the mass treatment is not sufficient to control the outbreak of VL in the population, additional control programs (such as vaccination) with treatment are required to control the VL disease outbreak.

Suggested Citation

  • Biswas, Santanu, 2017. "Mathematical modeling of Visceral Leishmaniasis and control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 546-556.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:546-556
    DOI: 10.1016/j.chaos.2017.09.005
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    References listed on IDEAS

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    1. Saifuddin, Md. & Biswas, Santanu & Samanta, Sudip & Sarkar, Susmita & Chattopadhyay, Joydev, 2016. "Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 270-285.
    2. Xing, Yi & Song, Lipeng & Sun, Gui-Quan & Jin, Zhen & Zhang, Juan, 2017. "Assessing reappearance factors of H7N9 avian influenza in China," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 192-204.
    3. Anette Stauch & Hans-Peter Duerr & Jean-Claude Dujardin & Manu Vanaerschot & Shyam Sundar & Martin Eichner, 2012. "Treatment of Visceral Leishmaniasis: Model-Based Analyses on the Spread of Antimony-Resistant L. donovani in Bihar, India," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 6(12), pages 1-8, December.
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    Cited by:

    1. Adamu, Elias M. & Patidar, Kailash C. & Ramanantoanina, Andriamihaja, 2021. "An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 171-190.
    2. Sharbayta, Sileshi Sintayehu & Buonomo, Bruno & d'Onofrio, Alberto & Abdi, Tadesse, 2022. "‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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