Vaccination and control measures on vector transmission dynamics: Modeling and simulation

References
[1] A. Abidemi, M.I. Abd Aziz, and R. Ahmad, Vaccination and vector control effect on dengue virus transmission
dynamics: Modelling and simulation, Chaos Solitons Fractals 133 (2020), 109648.
[2] R.M. Anderson and R.M. May, Spatial, temporal, and genetic heterogeneity in host populations and the design of
immunization programmes, Math. Med. Bio.: J. IMA 1 (1984), no. 3, 233–266.
[3] L. Billings, A. Fiorillo, and I.B. Schwartz, Vaccinations in disease models with antibody-dependent enhancement,
Math. Biosci. 211 (2008), no. 2, 265–281.
[4] K.W. Blayneh and S.R. Jang, A discrete sis-model for a vector-transmitted disease, Applicable Anal. 85 (2006),
no. 10, 1271–1284.
[5] V.G. Boltyanskiy, R.V. Gamkrelidze, Y.E.F. Mishchenko, and L.S. Pontryagin, Mathematical theory of optimal
proce[6] W.S. Burnside and A.W. Panton, The theory of equations: with an introduction to the theory of binary algebraic
forms, Longmans, Green and Co., Ltd., London, 1935.
[7] C. Cosner, J.C. Beier, R.S. Cantrell, D. Impoinvil, L. Kapitanski, M.D. Potts, A. Troyo, and S. Ruan, The effects
of human movement on the persistence of vector-borne diseases, J. Theor. Bio. 258 (2009), no. 4, 550–560.
[8] L. Coudeville and G.P. Garnett, Transmission dynamics of the four dengue serotypes in southern vietnam and
the potential impact of vaccination, PloS one 7 (2012), no. 12, e51244.
[9] I.V. Coutinho-Abreu and M. Ramalho-Ortigao, Transmission blocking vaccines to control insect-borne diseases:
a review, Mem. Instit. Oswaldo Cruz 105 (2010), no. 1, 1–12.
[10] K. Dietz and D. Schenzle, Proportionate mixing models for age-dependent infection transmission, J. Math. Bio.
22 (1985), no. 1, 117–120.
[11] M.K. Enduri and S. Jolad, Dynamics of dengue disease with human and vector mobility, Spat. Spatio-temporal
Epidemiol. 25 (2018), 57–66.
[12] T. Feng, Z. Qiu, and Y. Song, Global analysis of a vector-host epidemic model in stochastic environments, J.
Franklin Instit. 356 (2019), no. 5, 2885–2900.
[13] W.E. Fitzgibbon, J.J. Morgan, and G.F. Webb, An outbreak vector-host epidemic model with spatial structure:
The 2015–2016 zika outbreak in rio de janeiro, Theor. Bio. Med. Model. 14 (2017), no. 1, 1–17.
[14] L. Gao and H. Hethcote, Simulations of rubella vaccination strategies in china, Math. Biosci. 202 (2006), no. 2,
371–385.
[15] A.B. Gumel, C.C. McCluskey, and J. Watmough, An sveir model for assessing potential impact of an imperfect
anti-sars vaccine, Math. Biosci. Engin. 3 (2006), no. 3, 485.
[16] M. Haber, I.R.A.M. Longini Jr, and M.E. Halloran, Measures of the effects of vaccination in a randomly mixing
population, Int. J. Epidemiol. 20 (1991), no. 1, 300–310.
[17] K.P. Hadeler and J. M¨uller, Vaccination in age-structured populations i: The reproduction number, (1993).
[18] S.B. Halstead, F.X. Heinz, A.D.T. Barrett, and J.T. Roehrig, Dengue virus: molecular basis of cell entry and
pathogenesis, Vaccine 23 (2005), no. 7, 849—856.
[19] M. Iannelli, M. Martcheva, and X.-Z. Li, Strain replacement in an epidemic model with super-infection and perfect
vaccination, Math. Biosci. 195 (2005), no. 1, 23–46.
[20] T.K. Kar and S. Jana, Application of three controls optimally in a vector-borne disease–a mathematical study,
Commun. Nonlinear Sci. Numer. Simul. 18 (2013), no. 10, 2868–2884.
[21] M.Y. Li, J.R. Graef, L. Wang, and J. Karsai, Global dynamics of a seir model with varying total population size,
Math.Biosci. 160 (1999), no. 2, 191–213.
[22] D. Musso and D.J. Gubler, Zika virus: following the path of dengue and chikungunya?, Lancet 386 (2015),
no. 9990, 243–244.
[23] B. Shulgin, L. Stone, and Z. Agur, Pulse vaccination strategy in the sir epidemic model, Bull. Math. Bio. 60
(1998), no. 6, 1123–1148.
[24] H. Townson, M.B. Nathan, M. Zaim, P. Guillet, L. Manga, R. Bos, and M. Kindhauser, Exploiting the potential
of vector control for disease prevention, Bull. World Health Organ. 83 (2005), 942–947.
[25] J. Tumwiine, J.Y.T. Mugisha, and L.S. Luboobi, A host-vector model for malaria with infective immigrants, J.
Math. Anal. Appl. 361 (2010), no. 1, 139–149.
[26] P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), no. 1-2, 29–48.
[27] C. Vargas-De-Le´on, L. Esteva, and A. Korobeinikov, Age-dependency in host-vector models: the global analysis,
Appl. Math. Comput. 243 (2014), 969–981.
[28] J.X. Velascohernandez, A model for chagas disease involving transmission by vectors and blood transfusion, Theor.
Popul. Bio. 46 (1994), no. 1, 1–31.[29] A.L. Wilson, O. Courtenay, L.A. Kelly-Hope, T.W. Scott, W. Takken, S.J. Torr, and S.W. Lindsay, The importance of vector control for the control and elimination of vector-borne diseases, PLoS Neglect. Tropic. Diseases
14 (2020), no. 1, e0007831.
[30] Y. Xu, J.and Zhou, Hopf bifurcation and its stability for a vector-borne disease model with delay and reinfection,
Appl. Math. Model. 40 (2016), no. 3, 1685–1702.