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

Management strategies in a malaria model combining human and transmission-blocking vaccines
Pages: 977 - 1000, Issue 3, May 2017

doi:10.3934/dcdsb.2017049      Abstract        References        Full text (1164.8K)           Related Articles

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)

1 S. Ai, J. Li and J. Lu, Mosquito-stage-structured malaria models and their global dynamics, SIAM J. Appl. Math., 72 (2012), 1213-1237.       
2 M. Arevalo-Herrera, Y. Solarte, C. Marin, M. Santos, J. Castellanos, J. C. Beier and S. H. Valencia, Malaria transmission blocking immunity and sexual stage vaccines for interrupting malaria transmission in Latin America, Mem Inst Oswaldo Cruz, Rio de Janeiro., 106 (2011), 202-211.
3 J. Arino, A. Ducrot and P. Zongo, A metapopulation model for malaria with transmission-blocking partial immunity in hosts, J. Math. Biol., 64 (2012), 423-448.       
4 A. J. Birkett, V. S. Moorthy, C. Loucq, C. E. Chitnis and D. C. Kaslow, Malaria vaccine R&D in the Decade of Vaccines: Breakthroughs, challenges and opportunities, Vaccine, 31 (2013), B233-B243.
5 R. Carter, Transmission blocking malaria vaccines, Vaccine, 19 (2001), 2309-2314.
6 M. C. de Castro, Y. Yamagata, D. Mtasiwa, M. Tanner, J. Utzinger, J. Keiser and B. H. Singer, Integrated urban malaria control: A case study in Dar es Salaam, Tanzania, Am. J. Trop. Med. Hyg., 71 (2004), 103-117.
7 N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008), 1272-1296.       
8 O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R o in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.       
9 P. V. den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.       
10 X. Feng, S. Ruan, Z. Teng and K. Wang, Stability and backward bifurcation in a malaria transmission model with applications to the control of malaria in China, Math. Biosci., 266 (2015), 52-64.       
11 K. R Fister, S. Lenhart and J. S McNally, Optimizing Chemotherapy in an HIV Model, Electron. J. Diff. Eqns., (1998), 1-12.       
12 S. Gandon, M. J. Mackinnon, S. Nee and A. F. Read, Imperfect vaccines and the evolution of pathogen virulence, Nature, 414 (2001), 751-756.
13 A. B. Gumel, Causes of backward bifurcations in some epidemiological models, J. Math. Anal. Appl., 395 (2012), 355-365.       
14 M. E. Halloran and C. J. Struchiner, Modeling transmission dynamics of stage-specific malaria vaccines, Parasitology Today, 8 (1992), 77-85.
15 E coli has applications for malaria vaccine, HematologyTimes, 2014. Available from: http://www.hematologytimes.com/p_article.do?id=3845
16 S. Lenhart and J. T Workman, Optimal Control Applied to Biological Models, Chapman and Hall, 2007.
17 N. C. Ngonghalaa, G. A. Ngwa and M. I. Teboh-Ewungkem, Periodic oscillations and backward bifurcation in a model for the dynamics of malaria transmission, Math. Biosci., 240 (2012), 45-62.       
18 V. Nussenzweig, M. F. Good and A. V. Hill, Mixed results for a malaria vaccine, Nature Medicine, 17 (2011), 1560-1561.
19 L. S. Pontryagin, V. G. Boltyanskii, R . V . Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York, 2002.
20 O. Prosper and N. Ruktanonchai and M. Martcheva, Optimal vaccination and bednet maintenance for the control of malaria in a region with naturally acquired immunity, J Theor. Biol., 353 (2014), 142-156.       
21 K. Raghavendra, T. K. Barik, B. P. N. Reddy, P. Sharma and A. P. Dash, Malaria vector control: From past to future, Parasitology Research, 108 (2011), 757-779.
22 First Results of Phase 3 Trial of RTS,S/AS01 Malaria Vaccine in African Children, The RTS,S Clinical Trials Partnership, N. Engl. J. Med., 365 (2011), 1863-1875.
23 A Phase 3 Trial of RTS,S/AS01 Malaria Vaccine in African Infants, The RTS,S Clinical Trials Partnership, N. Engl. J. Med., 367 (2012), 2284-2295.
24 A. Saul, Mosquito stage, transmission blocking vaccines for malaria, Curr. Opin. Infect. Dis, 20 (2007), 476-481.
25 M. K. Seo, P. Baker and K. N. Ngo, Cost-effectiveness analysis of vaccinating children in Malawi with RTS,S vaccines in comparison with long-lasting insecticide-treated nets, Malaria Journal, 13 (2014), 66-76.
26 B. Sharma, Structure and mechanism of a transmission blocking vaccine candidate protein Pfs25 from P. falciparum: a molecular modeling and docking study, In Silico Biol., 8 (2008), 193-206.
27 R. J. Smith, Mathematical models of malaria - a review.Could Low-Efficacy Malaria Vaccines Increase Secondary Infections in Endemic Areas. Mathematical Modeling of Biological Systems Volume II Modeling and Simulation in Science, Engineering and Technology, Mathematical Modeling of Biological Systems, Volume II, 2 (2008), 3-9.
28 T. A. Smith, N. Chitnis and M. Tanner, Uses of mosquito-stage transmission-blocking vaccines against plasmodium falciparum, Trends in Parasitology, 27 (2011), 190-196.
29 T. Smith, G. F. Killeen, N. Maire, A. Ross, L. Molineaux, F. Tediosi, G. Hutton, J. Utzinger, K. Dietz and A. M. Tanner, Mathematical Modeling of The Impact of Malaria Vaccines on The Clinical Epidemiology and Natural History of Plasmodium Falciparum Malaria: Overview, Am. J. Trop. Med. Hyg., 75 (2006), 1-10.
30 M. T Teboh-Ewungkem, C. N. Podder and A. Gumel, Mathematical study of the role of gametocytes and an imperfect vaccine on malaria transmission dynamics, Bull. Math. Biol., 72 (2010), 63-93.       
31 N. J. White, A vaccine for malaria, N. Engl. J. Med., 365 (2011), 1926-1927.
32 World Health Organization 2000: Malaria transmission blocking vaccines: An ideal public good (2000), Available from: http://www.who.int/tdr/publications/tdr-research-publications/malaria-transmission-blocking-vaccines/en/.
33 World Malaria Report (2015), Available from: http://www.who.int/malaria/media/world-malaria-report-2015/en/.
34 R. Zhao and J. Mohammed-Awel, A mathematical model studying mosquito-stage transmission-blocking vaccines, Math. Biosci. Eng., 11 (2014), 1229-1245.       

Go to top