A Wolbachia infection model with free boundary

References

• S.Y. Mukherjee, Why Google’s verily is unleashing 20 million bacteria-infected mosquitoes in Fresno. Available at http://fortune.com/2017/07/14/google-verily-zika-mosquitoes/.
   Google Scholar
• G. Bian, Y. Xu, P. Lu, Y. Xie, Z. Xi and D. S. Schneider, The endosymbiotic bacterium wolbachia induces resistance to dengue virus in aedes aegypti, PLoS Pathog 6 (2010), p. e1000833. doi: 10.1371/journal.ppat.1000833
   PubMed Web of Science ®Google Scholar
• G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: analysis of a free boundary model, Netw. Het. Media 7 (2012), pp. 583–603.
   Web of Science ®Google Scholar
• R. Cantrell, C. Cosner, Spatial Ecology Via Reaction-Diffusion Equations, John Wiley & Sons, Chichester, 2003.
   Google Scholar
• J. Cao, W. Li and M. Zhao, A nonlocal diffusion model with free boundaries in spatial heterogeneous environment, J. Math. Anal. Appl. 449 (2017), pp. 1015–1035. doi: 10.1016/j.jmaa.2016.12.044
   Web of Science ®Google Scholar
• W. Ding, Y. Du and X. Liang, Spreading in space-time periodic media governed by a monostable equation with free boundaries, part 1: continuous initial functions, J. Differ. Equ. 262 (2017), pp. 4988–5021. doi: 10.1016/j.jde.2017.01.016
   Web of Science ®Google Scholar
• W. Ding, R. Peng and L. Wei, The diffusive logistic model with a free boundary in a heterogeneous time-periodic environment, J. Differ. Equ. 263 (2017), pp. 2736–2779. doi: 10.1016/j.jde.2017.04.013
   Web of Science ®Google Scholar
• N.C. Dom, A.H Ahmad and R. Ismail, Habitat characterization of Aedes Sp. breeding in Urban hotspot area, Procedia 85 (2013), pp. 100–109.
   Google Scholar
• Y. Du and Z. Guo, Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary II, J. Differ. Equ. 250 (2011), pp. 4336–4366. doi: 10.1016/j.jde.2011.02.011
   Web of Science ®Google Scholar
• Y. Du and Z. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal. 42 (2010), pp. 377–405. doi: 10.1137/090771089
   Web of Science ®Google Scholar
• Y. Du and Z. Lin, The diffusive competition model with a free boundary: invasion of a superior or inferior competitor, Discrete Contin. Dyn. Syst. Ser. B 19 (2014), pp. 3105–3132.
   Web of Science ®Google Scholar
• J. Guo and C. Wu, On a free boundary problem for a two-species weak competition system, J. Dynam. Differ. Equ. 24 (2012), pp. 873–895. doi: 10.1007/s10884-012-9267-0
   Web of Science ®Google Scholar
• M. Huang, J. Luo, L. Hu, B. Zheng and J. Yu, Assessing the efficiency of Wolbachia driven aedes mosquito suppression by delay differential equations, J. Theoret. Biol. 440 (2018), pp. 1–11. doi: 10.1016/j.jtbi.2017.12.012
   PubMed Web of Science ®Google Scholar
• M. Huang, M. Tang and J. Yu, Wolbachia infection dynamics by reaction-diffusion equations, Sci. China Math. 58 (2015), pp. 77–96. doi: 10.1007/s11425-014-4934-8
   Web of Science ®Google Scholar
• M. Huang, J. Yu, L. Hu and B. Zheng, Qualitative analysis for a wolbachia infection model with diffusion, Sci. China Math. 59 (2016), pp. 1249–1266. doi: 10.1007/s11425-016-5149-y
   Web of Science ®Google Scholar
• I. Iturbe-Ormaetxe, T. Walker and S.L. O'Neill, Wolbachia and the biological control of mosquito-borne disease, EMBO Rep. 12 (2011), pp. 508–518. doi: 10.1038/embor.2011.84
   PubMed Web of Science ®Google Scholar
• H. Laven, Cytoplasmic inheritance in culex, Nature 177 (1956), pp. 141–142. doi: 10.1038/177141a0
   Web of Science ®Google Scholar
• F. Li, X. Liang and W. Shen, Diffusive KPP equations with free boundaries in time almost periodic environments: II. spreading speeds and semi-wave solutions, J. Differ. Equ. 261 (2016), pp. 2403–2445. doi: 10.1016/j.jde.2016.04.035
   Web of Science ®Google Scholar
• Z. Lin, A free boundary problem for a predator-prey model, Nonlinearity 20 (2007), pp. 1883–1892. doi: 10.1088/0951-7715/20/8/004
   Web of Science ®Google Scholar
• Z. Lin and H. Zhu, Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary, J. Math. Biol. (2017), pp. 1–29.
   Web of Science ®Google Scholar
• A. Lunardi, Schauder theorems for linear elliptic and parabolic problems with unbounded coefficients in RN, Studia Math. 128(2) (1998), pp. 171–198. doi: 10.4064/sm-128-2-171-198
   Google Scholar
• E. Marris, Bacteria could be key to freeing South Pacific of mosquitoes, Nature 548(7665) (2017), pp. 17–18. doi:10.1038/548017a.
   PubMedGoogle Scholar
• C.J. McMeniman, R.V. Lane, B.N. Cass, A.W.C. Fong, M. Sidhu, Y.-F. Wang and S.L. O'Neill, Stable introduction of a life-shortening wolbachia infection into the mosquito aedes aegypti, Science 323 (2009), pp. 141–144. doi: 10.1126/science.1165326
   PubMed Web of Science ®Google Scholar
• H. Monobe and C. Wu, On a free boundary problem for a reaction-diffusion-advection logistic model in heterogeneous environment, J. Differ. Equ 261 (2016), pp. 6144–6177. doi: 10.1016/j.jde.2016.08.033
   Web of Science ®Google Scholar
• H. Ninomiya, Separatrices of competition-diffusion equations, J. Math. Kyoto Univ. 35 (1995), pp. 539–567. doi: 10.1215/kjm/1250518709
   Google Scholar
• H. Smith, Monotone Dynamical Systems, American Math Society, Providence, 1995.
   Google Scholar
• L. Song. (2017). China Focus: China's mosquito warriors fight global epidemic. Available at http://news.xinhuanet.com/english/2017-06/29/c_136403687.htm.
   Google Scholar
• C. Tian and S. Ruan, A free boundary problem for aedes aegypti mosquito invasion, Appl. Math. Model. 46 (2017), pp. 203–217. doi: 10.1016/j.apm.2017.01.050
   Web of Science ®Google Scholar
• M. Wang, On some free boundary problems of the prey-predator model, J. Differ. Equ. 256 (2014), pp. 3365–3394. doi: 10.1016/j.jde.2014.02.013
   Web of Science ®Google Scholar
• L. Wei, G. Zhang and M. Zhou, Long time behavior for solutions of the diffusive logistic equation with advection and free boundary, Calc. Var. Partial Differ. Equ. 55 (2016), pp. 1–34. doi: 10.1007/s00526-016-1039-y
   Web of Science ®Google Scholar
• Z. Xi, J. Dean, C. Khoo and S. Dobson, Generation of a novel wolbachia infection in aedes albopictus (asian tiger mosquito) via embryonic microinjection, Insect Biochem. Mol. Biol. 35 (2005), pp. 903–910. doi: 10.1016/j.ibmb.2005.03.015
   PubMed Web of Science ®Google Scholar
• Z. Xi and S. Dobson, Characterization of wolbachia transfection efficiency by using microinjection of embryonic cytoplasm and embryo homogenate, Appl. Environ. Microbiol. 71 (2005), pp. 3199–3204. doi: 10.1128/AEM.71.6.3199-3204.2005
   PubMed Web of Science ®Google Scholar
• Z. Xi, C. Khoo and S. Dobson, Wolbachia establishment and invasion in an aedes aegypti laboratory population, Science 310 (2005), pp. 326–328. doi: 10.1126/science.1117607
   PubMed Web of Science ®Google Scholar
• Z. Xi, C. Khoo and S. Dobson, Interspecific transfer of wolbachia into the mosquito disease vector aedes albopictus, Proc. Biol. Sci. 273 (2006), pp. 1317–1322.
   PubMed Web of Science ®Google Scholar
• J. Yu, Modeling mosquito population suppression based on delay differential equations, SIAM J. Appl. Math. 78 (2018), pp. 3168–3187. doi: 10.1137/18M1204917
   Web of Science ®Google Scholar
• J. Yu and B. Zheng, Modeling Wolbachia infection in mosquito population via discrete dynamical model, J. Differ. Equ. Appl. (2019) Available at https://doi.org/10.1080/10236198.2019.1669578.
   Web of Science ®Google Scholar
• Y. Zhang and M. Wang, A free boundary problem of the ratio-dependent prey-predator model, Appl. Anal. 94 (2015), pp. 2147–2167. doi: 10.1080/00036811.2014.979806
   Web of Science ®Google Scholar
• B. Zheng, M. Tang and J. Yu, Modeling wolbachia spread in mosquitoes through delay differential equations, SIAM J. Appl. Math. 74 (2014), pp. 743–770. doi: 10.1137/13093354X
   Web of Science ®Google Scholar
• B. Zheng and J. Yu, Characterization of Wolbachia enhancing domain in mosquitoes with imperfect maternal transmission, J. Biol. Dyn. 12 (2018), pp. 596–610. doi: 10.1080/17513758.2018.1499969
   PubMed Web of Science ®Google Scholar
• P. Zhou and D. Xiao, The diffusive logistic model with a free boundary in heterogeneous environment, J. Differ. Equ. 256 (2014), pp. 1927–1954. doi: 10.1016/j.jde.2013.12.008
   Web of Science ®Google Scholar
• L. Zhou, S. Zhang and Z. Liu, An evolutional free-boundary problem of a reaction-diffusion-advection system, Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), pp. 615–648. doi: 10.1017/S0308210516000226
   Google Scholar
• L. Zhou, S. Zhang and Z. Liu, Pattern formations for a strong interacting free boundary problem, Acta Appl. Math. 148 (2017), pp. 121–142. doi: 10.1007/s10440-016-0081-2
   Web of Science ®Google Scholar