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Tianyuan Hengyang Workshop 2020

The blood-stage dynamics of malaria infection with immune response

, ORCID Icon &
Pages 294-319 | Received 30 Aug 2021, Accepted 30 Nov 2021, Published online: 22 Dec 2021

References

  • Z.G. Bai, R. Peng and X.Q. Zhao, A reaction-diffusion malaria model with seasonality and incubation period, J. Math. Biol. 77 (2018), pp. 201–228.
  • Z.G. Chang, J. Ning and Y.Y Zhang, et al. The TatD-like DNase of Plasmodium is a virulence factor and a potential malaria vaccine candidate, Nat. Commun. 7 (2016), pp. 11537–11546.
  • C. Chiyaka, W. Garira and S. Dube, Modelling immune response and drug therapy in human malaria infection, Comput. Math. Methods Med. 9(2) (2008), pp. 143–163.
  • C. Cosner, J.C. Beier and R.S. Cantrell, et al. The effects of human movement on the persistence of vector-borne diseases, J. Theor. Biol. 258(4) (2009), pp. 550–560.
  • Q. Ding, J. Liu and Z.M. Guo, Dynamics of a malaria infection model with time delay, Math. Biosci. Eng. 16(5) (2009), pp. 4885–4907.
  • X.M. Feng, S.G. Ruan and Z.D. Teng, et al. Stability and backward bifurcation in a malaria transmission model with applications to the control of malaria in China, Math. Biosci. 266 (2015), pp. 52–64.
  • J.K. Hale, Asymptotic Behavior of Dissipative Systems, American Mathematical Society, Providence, RI, 1988.
  • B.D. Hassard and N.D. Kazarinoff, Theory and Applications of Hopf Bifurcation, Cambridge University Press, Cambridge, 1981.
  • J.M. Heffernan, R.J. Smith and L.M. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface 2 (2005), pp. 281–293.
  • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, New York, 1981.
  • Y. Li, S.G. Ruan and D.M. Xiao, The within-host dynamics of malaria infection with immune response, Math. Biosci. Eng. 8(4) (2011), pp. 999–1018.
  • Y. Lou and X.Q. Zhao, The periodic Ross–Macdonald model with diffusion and advection, Appl. Anal.89(7) (2010), pp. 1067–1089.
  • Y. Lou and X.Q. Zhao, A reaction-diffusion malaria model with incubation period in the vector population, J. Math. Biol. 62 (2011), pp. 543–568.
  • R.J. Martin and H.L. Smith, Abstract functional differential equations and reaction-diffusion systems, Trans. Am. Math. Soc. 321 (1990), pp. 1–44.
  • F. McKenzie and H. Bossert, An integrated model of Plasmodium falciparum dynamics, J. Theor. Biol. 232 (2005), pp. 411–426.
  • S.G. Ruan and W.D. Wang, Dynamical behavior of an epidemic model with a nonlinear incidence rate, J. Differ. Equ. 188 (2003), pp. 135–163.
  • H.L. Smith, Monotone dynamical systems: An introduction to the theory of competitive and cooperative systems, Am. Math. Soc. Ebooks Progr. 41(5) (1995), pp. 174.
  • R.W. Snow, C.A. Guerra and A.M. Noor, et al. The global distribution of clinical episodes of Plasmodium falciparum malaria – Supplementary Information, Nature 434(7030) (2005), pp. 214–217.
  • P.K. Streatfield, W.A. Khan and A. Bhuiya, et al. Cause-specific childhood mortality in Africa and Asia: evidence from INDEPTH health and demographic surveillance system sites, Global Health Action7 (2014), pp. 25362.
  • WHO. Malaria, 2008, Available from: http://www.who.int/malaria/en.
  • X.N. Wang and X.F. Zou, Modeling the potential role of engineered symbiotic bacteria in malaria control, Bull. Math. Biol. 81(7) (2019), pp. 2569–2595.
  • J.H. Wu, Theory and Applications of Partial Functional Differential Equations, Applied Mathematical Science, Springer, Berlin, 1996.
  • D.M. Xiao and Y. Yang, Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models, Discr. Cont. Dyn. Syst. 13(1) (2009), pp. 195–211.
  • Y.Y. Xiao and X.F. Zou, Can multiple malaria species co-persist?, SIAM J. Appl. Math. 73(1) (2013), pp. 351–373.
  • Z.T. Xu and X.Q. Zhao, A vector-bias malaria model with incubation period and diffusion, Discr. Cont. Dyn. Syst. 17(7) (2013), pp. 2615–2634.