Malaria modeling and optimal control using sterile insect technique and insecticide-treated net

References

• Bill & Melinda Gates Foundation. What We Do – Malaria Strategy Overview. Available from: https://www.gatesfoundation.org/What-We-Do/Global-Health/Malaria.
   Google Scholar
• CDC Parasites- Malaria. Available from: https://www.cdc.gov/parasites/malaria/index.html.
   Google Scholar
• Sherman IW. Twelve diseases that changed our world. Washington (DC): American Society of Microbiology Press; 2007.
   Google Scholar
• The President's Malaria Initiative. Available from: https://www.pmi.gov.
   Google Scholar
• World Malaria Report 2020. Available from: https://www.who.int/publications/i/item/9789240015791.
   Google Scholar
• Abdul-Ghani R, Farag HF, Allam AF, et al. Measuring resistant-genotype transmission of malaria parasites: challenges and prospects. Parasitol Res. 2014;113:1481–1487.
   PubMed Web of Science ®Google Scholar
• Alonso PL, Brown G, Arevalo-Herrera M, et al. A research agenda to underpin malaria eradication. PLoS Med. 2011;8:e1000406.
   PubMed Web of Science ®Google Scholar
• Brogdon WG, McAllister JC. Insecticide resistance and vector control. J Agromedicine. 1999;6:41–58.
   Google Scholar
• Coutinho-Abreu IV, Zhu KY, Ramalho-Ortigao M. Transgenesis and paratransgenesis to control insect-borne diseases: current status and future challenges. Parasitol Int. 2010;58:1–8.
   Web of Science ®Google Scholar
• Hurwitz I, Fieck A, Read A, et al. Paratransgenic control of vector borne diseases. Int J Biol Sci. 2011;7:1334–1344.
   PubMed Web of Science ®Google Scholar
• Ito J, Ghosh A, Moreira LA, et al. Transgenic anopheline mosquitoes impaired in transmission of a Malaria parasite. Nature. 2002;417:452–455.
   PubMed Web of Science ®Google Scholar
• Knipling EF. Possibilities of insect control or eradication through the use of sexually sterile males. J Econ Entomol. 1955;48:459–462.
   Web of Science ®Google Scholar
• Zheng X, Zhang D, Li Y, et al. Incompatible and sterile insect techniques combined eliminate mosquitoes. Nature. 2019;572:56–61.
   PubMed Web of Science ®Google Scholar
• Walker T, Johnson PH, Moreika LA, et al. The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations. Nature. 2011;476:450–453.
   PubMed Web of Science ®Google Scholar
• Xi Z, Khoo CCH, Dobson SI. Wolbachia establishment and invasion in an Aedes aegypti laboratory population. Science. 2005;310:326–328.
   PubMed Web of Science ®Google Scholar
• Alphey L. Genetic control of mosquitoes. Annu Rev Entomol. 2014;59:205–224.
   PubMed Web of Science ®Google Scholar
• Winskill P, Harris AF, Morgan SA, et al.. Genetic control of Aedes aegypti: data-driven modelling to assess the effect of releasing different life stages and the potential for long-term suppression. Parasit Vectors. 2014;7:3.
   PubMed Web of Science ®Google Scholar
• Yin H, Yang C, Zhang X, et al. The impact of releasing sterile mosquitoes on malaria transmission. Discrete Contin Dyn Syst B. 2018;23:3837–3853.
   Web of Science ®Google Scholar
• Huang M, Tang M, Yu J. Wolbachia infection dynamics by reaction–diffusion equations. Sci China Math. 2015;58:77–96.
   Web of Science ®Google Scholar
• Zhang X, Tang S, Cheke RA. Models to assess how best to replace dengue virus vectors with Wolbachia-infected mosquito populations. Math Biosci. 2015;269:164–177.
   PubMed Web of Science ®Google Scholar
• Zheng B, Tang M, Yu J. Modeling Wolbachia spread in mosquitoes through delay differential equations. SIAM J Appl Math. 2014;74:743–770.
   Web of Science ®Google Scholar
• Anguelov R, Dumont Y, Lubuma J. Mathematical modeling of sterile insect technology for control of anopheles mosquito. Comput Math Appl. 2012;64:374–389.
   Web of Science ®Google Scholar
• Cai L, Ai S, Li J. Dynamics of mosquitoes populations with different strategies of releasing sterile mosquitoes. SIAM J Appl Math. 2014;75:1223–1237.
   Google Scholar
• Cardona-Salgado D, Campo-Duarte DE, Sepulveda-Salcedo LS, et al. Wolbachia-based biocontrol for dengue reduction using dynamic optimization approach. Appl Math Model. 2020;82:125–149.
   Web of Science ®Google Scholar
• Dumont Y, Tchuenche JM. Mathematical studies on the sterile insect technique for the Chikungunya disease and Aedes albopictus. J Math Biol. 2012;65:809–854.
   PubMed Web of Science ®Google Scholar
• Fister KR, McCarthy ML, Oppenheimer SF. Diffusing wild type and sterile mosquitoes in an optimal control setting. Math Biosci. 2018;302:100–115.
   PubMed Web of Science ®Google Scholar
• Huang J, Ruan S, Yu P, et al. Bifurcation analysis of a mosquito population model with a saturated release rate of sterile mosquitoes. SIAM J Appl Dyn Syst. 2019;18:939–972.
   Web of Science ®Google Scholar
• Lees RS, Gilles JRL, Hendrichs J, et al. Back to the future: the sterile insect technique against mosquito disease vectors. Curr Opin Insect Sci. 2015;10:156–162.
   PubMed Web of Science ®Google Scholar
• Multerer L, Smith T, Chitnis N. Modeling the impact of sterile males on an Aedes aegypti population with optimal control. Math Biosci. 2019;311:91–102.
   PubMed Web of Science ®Google Scholar
• Stone CM, Somers M. Transient population dynamics of mosquitoes during sterile male releases: modelling mating behaviour and perturbations of life history parameters. PLoS ONE. 2013;8(9):e76228.
   PubMed Web of Science ®Google Scholar
• Blimana PA, Cardona-Salgado D, Dumont Y, et al. Implementation of control strategies for sterile insect techniques. Math Biosci. 2019;314:43–60.
   PubMed Web of Science ®Google Scholar
• Cai L, Huang J, Song X, et al. Bifurcation analysis of a mosquito population model for proportional releasing sterile mosquitoes. Discrete Contin Dyn Syst B. 2019;24:6279–6295.
   Web of Science ®Google Scholar
• Cai L, Ai S, Fan G. Dynamics of delayed mosquitoes populations models with two different strategies of releasing sterile mosquitoes. Math Biosci Eng. 2018;15(5):1181–1202.
   PubMed Web of Science ®Google Scholar
• Li J, Cai L, Li Y. Stage-structured wild and sterile mosquito population models and their dynamics. J Biol Dyn. 2017;11:79–101.
   PubMed Web of Science ®Google Scholar
• Yu JS, Li Jia. Global asymptotic stability in an interactive wild and sterile mosquito model. J Differ Equ. 2020;269:6193–6215.
   Web of Science ®Google Scholar
• Yin H, Yang C, Zhang X, et al. Dynamics of malaria transmission model with sterile mosquitoes. J Biol Dyn. 2018;12:577–595.
   PubMed Web of Science ®Google Scholar
• Castro D, Yamagata MC, et al. Integrated urban malaria control: a case study in Dar es Salaam. Tanzania Am J Trop Med Hyg. 2004;71:103–117.
   PubMed Web of Science ®Google Scholar
• Okosuna KO, Ouifki R, Marcus N. Optimal control analysis of a malaria disease transmission model that includes treatment and vaccination with waning immunity. BioSyst. 2011;106:136–145.
   Web of Science ®Google Scholar
• Raghavendra K, Barik TK, et al. Malaria vector control: from past to future. Parasitol Res. 2011;108:757–779.
   PubMed Web of Science ®Google Scholar
• Agusto FB, Marcus N, Okosun KO. Application of optimal control to the epidemiology of malaria. Electron J Differ Equ. 2012;81:1–22.
   Google Scholar
• Khamis D, Mouden CEl., Kura K, et al. Optimal control of malaria: combining vector interventions and drug therapies. Malar J. 2018;17:174.
   PubMed Web of Science ®Google Scholar
• Rafikov M, Bevilacqua LJ, Wyse A. Optimal control strategy of malaria vector using genetically modified mosquitoes. J Theor Biol. 2009;258:418–425.
   PubMed Web of Science ®Google Scholar
• Thome RCA, Yang HM, Esteva L. Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide. Math Biosci. 2010;223:12–23.
   PubMed Web of Science ®Google Scholar
• Chitnis N, Cushing JM, Hyman JM. Bifurcation analysis of a mathematical model for malaria transmission. SIAM J Appl Math. 2006;67:24–45.
   Web of Science ®Google Scholar
• Chitnis N, Hyman JM, Cushing JM. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull Math Biol. 2008;70:1272–1296.
   PubMed Web of Science ®Google Scholar
• Koella JC. On the use of mathematical models of malaria transmission. Acta Trop. 1991;49:1–25.
   PubMed Web of Science ®Google Scholar
• Dietz K, Molineaux L, Thomas A. A malaria model tested in the African savannah. Bull World Health Organ. 1974;50:347–357.
   PubMed Web of Science ®Google Scholar
• Mandal S, Sarkar RR, Sinha S. Mathematical models of malaria: a review. Malar J. 2011;10:1–19.
   PubMed Web of Science ®Google Scholar
• Li J. New revised simple models for interactive wild and sterile mosquito populations and their dynamics. J Biol Dyn. 2017;11:316–333.
   PubMed Web of Science ®Google Scholar
• van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci. 2002;180:29–48.
   PubMed Web of Science ®Google Scholar
• Barrios E, Lee S, Vasilieva O. Assessing the effects of daily commuting in two-patch dengue dynamics: a case study of Cali, Colombia. J Theor Biol. 2018;453:14–39.
   PubMed Web of Science ®Google Scholar
• Martcheva M. Introduction to mathematical epidemiology. New York (NY): Springer; 2015. (Texts in applied mathematics; 61).
   Google Scholar
• Lukes DL. Differential equations: classical to controlled. New York (NY): Academic Press; 1982.
   Google Scholar
• Fleming WH, Rishel RW. Deterministic and stochastic optimal control. New York (NY): Springer-Verlag; 1975.
   Google Scholar
• Lenhart S, Workman JT. Optimal control applied to biological models. Boca Raton: CRC Press; 2007.
   Google Scholar
• Pontragin LS, Gamkrelize RV, Boltyanskii VG, et al. The mathematical theory of optimal processes. New York: Wiley; 1962.
   Google Scholar