Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Management strategies in a malaria model combining human and transmission-blocking vaccines

Pages: 977 - 1000, Volume 22, Issue 3, May 2017      doi:10.3934/dcdsb.2017049

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Jemal Mohammed-Awel - Department of Mathematics and Computer Science, Valdosta State University, Valdosta, GA, 31698, United States (email)
Ruijun Zhao - Department of Mathematics and Statistics, Minnesota State University, Mankato, Mankaot, MN, 56001, United States (email)
Eric Numfor - Department of Mathematics, Augusta University, Augusta, GA 30912, United States (email)
Suzanne Lenhart - Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300, United States (email)

Abstract: We propose a new mathematical model studying control strategies of malaria transmission. The control is a combination of human and transmission-blocking vaccines and vector control (larvacide). When the disease induced death rate is large enough, we show the existence of a backward bifurcation analytically if vaccination control is not used, and numerically if vaccination is used. The basic reproduction number is a decreasing function of the vaccination controls as well as the vector control parameters, which means that any effort on these controls will reduce the burden of the disease. Numerical simulation suggests that the combination of the vaccinations and vector control may help to eradicate the disease. We investigate optimal strategies using the vaccinations and vector controls to gain qualitative understanding on how the combinations of these controls should be used to reduce disease prevalence in malaria endemic setting. Our results show that the combination of the two vaccination controls integrated with vector control has the highest impact on reducing the number of infected humans and mosquitoes.

Keywords:  Stability, malaria, transmission-blocking vaccine, optimal control, differential equations.
Mathematics Subject Classification:  Primary: 92D30; Secondary: 49J15.

Received: August 2015;      Revised: September 2016;      Available Online: January 2017.