A Mathematical Model for the Transmission Dynamics of Lymphatic Filariasis with Intervention Strategies

  • S. M. SimelaneEmail author
  • P. M. Mwamtobe
  • S. Abelman
  • J. M. Tchuenche
Regular Article


This manuscript considers the transmission dynamics of lymphatic filariasis with some intervention strategies in place. Unlike previously developed models, our model takes into account both the exposed and infected classes in both the human and mosquito populations, respectively. We also consider vaccinated, treated and recovered humans in the presented model. The global dynamics of the proposed model are completely determined by the basic (\({\mathcal {R}}_0\)) and effective reproduction numbers (\({\mathcal {R}}_e\)). We then use Lyapunov function theory to find the sufficient conditions for global stability of both the disease-free equilibrium and endemic equilibrium. The Lyapunov functions show that when the basic reproduction number is less than or equal to unity, the disease-free equilibrium is globally asymptotically stable, and when it is greater than unity then the endemic equilibrium is also globally asymptotically stable. Finally, numerical simulations are carried out to investigate the effects of the intervention strategies and key parameters to the spread of lymphatic filariasis. The numerical simulations support the analytical results and illustrate possible model behavioral scenarios.


Lymphatic filariasis Treatment of infected-acute individuals Insecticide residual spraying Reproduction number 



The reviewers are thanked for their careful reading of our manuscript. Their useful comments have resulted in an improved manuscript.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Applied MathematicsUniversity of JohannesburgAuckland ParkSouth Africa
  2. 2.Department of Applied Studies, Malawi Institute of TechnologyMalawi University of Science and TechnologyLimbeMalawi
  3. 3.School of Computer Science and Applied MathematicsUniversity of the Witwatersrand, JohannesburgWitsSouth Africa

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