Bulletin of Mathematical Biology

, Volume 81, Issue 11, pp 4366–4411 | Cite as

Analysis of Malaria Control Measures’ Effectiveness Using Multistage Vector Model

  • Jean Claude KamgangEmail author
  • Christopher Penniman Thron
Special Issue: Mathematical Epidemiology


We analyze an epidemiological model to evaluate the effectiveness of multiple means of control in malaria-endemic areas. The mathematical model consists of a system of several ordinary differential equations and is based on a multi-compartment representation of the system. The model takes into account the multiple resting–questing stages undergone by adult female mosquitoes during the period in which they function as disease vectors. We compute the basic reproduction number \(\mathcal R_0\) and show that if \(\mathcal R_0\le 1\), the disease-free equilibrium is globally asymptotically stable (GAS) on the nonnegative orthant. If \(\mathcal R_0>1\), the system admits a unique endemic equilibrium (EE) that is GAS. We perform a sensitivity analysis of the dependence of \(\mathcal R_0\) and the EE on parameters related to control measures, such as killing effectiveness and bite prevention. Finally, we discuss the implications for a comprehensive, cost-effective strategy for malaria control.


Epidemiological model Malaria Basic reproduction number Lyapunov function Global asymptotic stability Control strategies Sensitivity analysis 

Mathematics Subject Classification

34C60 34D20 34D23 92D30 



The second author would like to thank the Fulbright U.S. Scholar program and the International Mathematicians Union’s VLP program for supporting visits to ENSAI which made this research possible. The authors would also like to thank the reviewers for helpful comments that led to significant improvements in the quality and clarity of this paper.


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesENSAI – University of N’GaoundéréN’GaoundéréCameroon
  2. 2.Department of Sciences and MathematicsTexas A&M University – Central TexasKilleenUSA

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