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Research Article

Complexity of host-vector dynamics in a two-strain dengue model

ORCID Icon & ORCID Icon
Pages 35-72 | Received 28 Jan 2020, Accepted 06 Dec 2020, Published online: 28 Dec 2020

References

  • M. Aguiar, B.W. Kooi, and N. Stollenwerk, Epidemiology of dengue fever: a model with temporary cross-immunity and possible secondary infection shows bifurcations and chaotic behaviour in wide parameter regions, Math Model Nat. Phenom. 3 (2008), pp. 48–70.
  • M. Aguiar, S. Ballesteros, B.W. Kooi, and N. Stollenwerk, The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis, J. Theor. Biol. 289 (2011), pp. 181–196.
  • S. Bedini, G. Flamini, R. Ascrizzi, F. Venturi, G. Ferroni, A. Bader, J. Girardi, and B. Conti, Essential oils sensory quality and their bioactivity against the mosquito Aedes albopictus, Sci. Rep. 8 (2018), pp. 17857.
  • L. Billings, I.B. Schwartz, L.B. Shaw, M. McCrary, D.S. Burke, and D.A.T. Cummings, Instabilities in multiserotype disease models with antibody-dependent enhancement, J. Theor. Biol. 246 (2007), pp. 18–27.
  • B. Buonomo and R. DellaMarca, Optimal bed net use for a dengue disease model with mosquito seasonal pattern, Math. Meth. Appl. Sci. 41(2) (2018), pp. 573–592.
  • L.B. Carrington and C.P. Simmons, Human to mosquito transmission of dengue viruses, Front. Immunol. 5 (2014), pp. 290.
  • K.H. Changal, A.H. Raina, A. Raina, M. Raina, R. Bashir, M. Latief, T. Mir, and Q.H. Changal, Differentiating secondary from primary dengue using IgG to IgM ratio in early dengue: an observational hospital based clinico-serological study from north india, BMC Infect. Dis. 16 (2016), pp. 715.
  • M.R.W. de Valdez, D. Nimmo, J. Betz, H.-F. Gong, A.A. James, L. Alphey, and W.C. Black IV, Genetic elimination of dengue vector mosquitoes, Proc. Natl Acad. Sci. USA 108(12) (2011), pp. 4772–4775.
  • O. Diekmann and J.A.P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases, Wiley series in Mathematical and Computational Biology. Wiley, Chichester, 2000.
  • O. Diekmann, J.A.P. Heesterbeek, and J.A.J. Metz, On the definition and the computation of the basic reproduction ratio r0 in models for infectious diseases in heterogeneous populations, J. Math. Biol.28 (1990), pp. 365–382.
  • O. Diekmann, M. de Jong, A. de Koeijer, and P. Reijnders, The force of infection in populations of varying size: a modelling problem. Technical Report AM-R9403, Centrum voor Wiskunde en Informatica, 1994.
  • E.J. Doedel and B. Oldeman, AUTO 07p: Continuation and bifurcation software for ordinary differential equations, Technical report, Concordia University, Montréal, Canada, 2012.
  • V. Duong, L. Lambrechts, R.E. Paul, S. Ly, R.S. Lay, K.C. Long, R. Huy, A. Tarantola, T.W. Scott, A. Sakuntabhai, and P. Buchya, Asymptomatic humans transmit dengue virus to mosquitoes, Proc. Natl Acad. Sci. USA 11 (2015), pp. 14688–14693.
  • L. Esteva and C. Vargas, Analysis of a dengue disease transmission model, Math. Biosci. 150(2) (1998), pp. 131–151.
  • Z. Feng and J.X. Velasco-Hernandez, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol. 35 (1997), pp. 523–544.
  • N. Fenichel, Persistence and smoothness of invariant manifolds for flows, Indiana. U Math. J. 21 (1971), pp. 193–226.
  • N. Fenichel, Geometric singular perturbation theory, J. Differ. Equ. 31 (1979), pp. 53–98.
  • N. Ferguson, R. Anderson, and S. Gupta, The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens, Proc. Natl Acad. Sci. USA 96(9) (1999), pp. 790–794.
  • T. Götz, K.P. Wijaya, and E. Venturino, Introducing seasonality in an SIR-UV epidemic model: an application to dengue. 18th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2018, Wiley Online Library, 2018
  • M.G. Guzman, M. Alvarez, and S.B. Halstead, Secondary infection as a risk factor for dengue hemorrhagic fever/dengue shock syndrome: an historical perspective and role of antibody-dependent enhancement of infection, Arch. Virol. 158 (2013), pp. 1445–59.
  • G. Hek, Geometric singular perturbation theory in biological practice, J. Math. Biol. 60 (2010), pp. 347–386.
  • B.W. Kooi, M. Aguiar, and N. Stollenwerk, Bifurcation analysis of a family of multi-strain epidemiology models, J. Comput. Appl. Math. 252 (2013), pp. 148–158.
  • B.W. Kooi, M. Aguiar, and N. Stollenwerk, Analysis of an asymmetric two-strain dengue model, Math. Biosci. 248 (2014), pp. 128–139.
  • A. Korobeinikov, Lyapunov functions and global properties for SEIR and SEIS epidemic models, Math. Med. Biol. 21 (2004), pp. 75–83.
  • Y.A. Kuznetsov, Elements of Applied Bifurcation Theory, 3rd ed., Vol. 112 of Applied Mathematical Sciences. Springer-Verlag, New York, 2004.
  • N.M. Nguyen, D. Thi Hue Kien, T.V. Tuan, N.T.H. Quyen, C.N.B. Tran, L. Vo Thi, D.L. Thi, H.L.Nguyen, J.J. Farrar, E.C. Holmes, M.A. Rabaa, J.E. Bryant, T.T. Nguyen, H.T.C. Nguyen, L.T.H.Nguyen, M.P. Pham, H.T. Nguyen, T.T.H. Luong, B. Wills, C.V.V. Nguyen, M. Wolbers, and C.P.Simmons, Host and viral features of human dengue cases shape the population of infected and infectious Aedes aegypti mosquitoes, Proc. Natl Acad. Sci. USA 110 (2013), pp. 9072–9077.
  • P. Rashkov, E. Venturino, M. Aguiar, N. Stollenwerk, and B.W. Kooi, On the role of vector modeling in a minimalistic epidemic model, Math. Biosci. Eng. 5(16) (2019), pp. 4314–4338.
  • M. Recker, K.B. Blyuss, C.P. Simmons, T.T. Hien, B. Wills, J. Farrar, and S. Gupta, Immunological serotype interactions and their effect on the epidemiological pattern of dengue, Proc. R. Soc. B276(1667) (2009), pp. 2541–2548.
  • F. Rocha, M. Aguiar, M. Souza, and N. Stollenwerk, Time-scale separation and centre manifold analysis describing vector-borne disease dynamics, Int. J. Comput. Math. 90(10) (2013), pp. 2105–2125.
  • H.S. Rodrigues, M.T.T. Monteiro, D.F.M. Torres, A.C. Silva, C. Sousa, and C. Conceio, Dengue in Madeira island. In Dynamics, Games and Science -- International Conference and Advanced School Planet Earth, J.-P. Bourguignon, R. Jeltsch, A. A. Pinto, and M. Viana, eds., DGS II, Portugal, pp. 593–605, August 28–September 6, 2013.
  • H.S. Rodrigues, M.T.T. Monteiro, and D.F.M. Torres, Seasonality effects on dengue: basic reproduction number, sensitivity analysis and optimal control, Math. Meth. Appl. Sci. 39(16) (2016), pp. 4671–4679.
  • D. Ruelle and F. Takens, On the nature of turbulence, Comm. Math. Phys. 20 (1971), pp. 167–192.
  • Q.A. ten Bosch, H.E. Clapham, L. Lambrechts, V. Duong, P. Buchy, B.M. Althouse, A.L. Lloyd, L.A. Waller, A.C. Morrison, U. Kitron, G.M. Vazquez-Prokopec, T.W. Scott, and T.A. Perkins, Contributions from the silent majority dominate dengue virus transmission, PLoS Pathog. 14(5) (2018), p. e1006965.
  • H. Tian, Z. Sun, N.R. Faria, J. Yang, B. Cazelles, S. Huang, B. Xu, Q. Yang, O.G. Pybus, and B. Xu, Increasing airline travel may facilitate co-circulation of multiple dengue virus serotypes in Asia, PLoS Negl. Trop. Dis. 11(8) (2017), p. e0005694.
  • WHO, Fact sheet: dengue and severe dengue. Available at https://www.who.int/. Accessed 4 November 2019.
  • T.-T. Zheng and L.-F. Nie, Modelling the transmission dynamics of two-strain dengue in the presence awareness and vector control, J. Theor. Biol. 443 (2018), pp. 82–91.