Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Angewandte Mathematik - Numerische Analysis

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Mathematical Modelling of Zika Virus Epidemics


Bachelor Thesis Mathematics



Betreuung

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Description

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Key Words

Zika virus, (discrete) models of epidemics, disease outbreaks, nonstandard FD methods

Literature:

  1. E. Addai, L. Zhang, J. Ackora-Prah, J.F. Gordon, J.K.K. Asamoah, and J.F. Essel, Fractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets, Physica A: Stat. Mech. Appl. 603 (2022), 127809.
  2. F.B. Agusto, S. Bewick, and W.F. Fagan, Mathematical model of Zika virus with vertical transmission, Infect. Dis. Model. 2(2) (2017), 244-267.
  3. F.B. Agusto, S. Bewick, and W.F. Fagan, Mathematical model for Zika virus dynamics with sexual transmission route, Ecolog. Compl. 29 (2017), 61-81.
  4. A. Ali, Q. Iqbal, J.K.K. Asamoah, and S. Islam, Mathematical modeling for the transmission potential of Zika virus with optimal control strategies, Europ. Phys. J. Plus, 137(1) (2022), 1-30.
  5. A. Ali, S. Islam, M.R. Khan, S. Rasheed, F.M. Allehiany, J. Baili, M.A. Khan, and H. Ahmad, Dynamics of a fractional order Zika virus model with mutant, Alexandria Engrg. J. 61(6) (2022), 4821-4836.
  6. A. Ali, F.S. Alshammari, S. Islam, M.A. Khan, and S. Ullah, Modeling and analysis of the dynamics of novel coronavirus (COVID-19) with Caputo fractional derivative, Results in Physics 20 (2021), 103669.
  7. H.M. Ali and I.G. Ameen, Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions, Chaos, Solitons \& Fractals 146 (2021), 110864.
  8. E.O. Alzahrani, W. Ahmad, M.A. Khan, and S.J. Malebary, Optimal control strategies of Zika virus model with mutant, Commun. Nonlin. Sci. Numer. Simul. 93 (2021), 105532.
  9. Diego F. Aranda L., G. Gonzalez-Parra, and T. Benincasa, Mathematical modeling and numerical simulations of Zika in Colombia considering mutation, Math. Comput. Simul. 163 (2019), 1-18.
  10. R. Becker, Animal models to study whether Zika causes birth defects, Nat. Med. 22(3) (2016), 225-227.
  11. R. Begum, O. Tun, H. Khan, H. Gulzar, and A. Khan, A fractional order Zika virus model with Mittag-Leffler kernel, Chaos, Solitons & Fractals 146 (2021), 110898.
  12. S. Berkhahn and M. Ehrhardt, A Physics-Informed Neural Network to Model COVID-19 Infection and Hospitalization Scenarios, accepted: Advances in Continuous and Discrete Models: Theory and Applications, 2022.
  13. K. Best and A.S. Perelson, Mathematical modeling of within-host Zika virus dynamics, Immunol. Rev. 285(1) (2018), 81-96.
  14. S.K. Biswas, U. Ghosh, and S. Sarkar, Mathematical model of Zika virus dynamics with vector control and sensitivity analysis, Infect. Dis. Model. 5 (2020), 23-41.
  15. E. Bonyah and K.O. Okosun, Mathematical modeling of Zika virus, Asian Pac. J. Trop. Dis. 6(9) (2016), 673-679.
  16. E. Bonyah, M.A. Khan, K.O. Okosun, and J.F. Gómez-Aguilar, On the co-infection of dengue fever and Zika virus, Optim. Contr. Appl. Meth. 40(3) (2019), 394-421.
  17. E. Bonyah, M.A. Khan, K.O. Okosun, and S. Islam, A theoretical model for Zika virus transmission, PloS one, 12(10) (2017), e0185540.
  18. J.P.T. Boorman and J.S. Porterfield, A simple technique for infection of mosquitoes with viruses, transmission of Zika virus, Trans. Roy. Soc. Trop. Med. Hyg. 50(3) (1956), 238-242.
  19. L. Bouzid and O. Belhamiti, Effect of seasonal changes on predictive model of bovine babesiosis transmission, Int. J. Model. Simul. Sci. Comput. 8(4) (2017), 1-17.
  20. F. Brauer and C. Castillo-Chávez, Basic Ideas of Mathematical Epidemiology, Mathematical Models in Population Biology and Epidemiology, Springer, 2001, pp. 275-337.
  21. Y. Cai, K. Wang, and W. Wang, Global transmission dynamics of a Zika virus model, Appl. Math. Lett. 92 (2019), 190-195.
  22. C.J. Carlson, E.R. Dougherty, and W. Getz, An ecological assessment of the pandemic threat of Zika virus, PLoS Negl. Trop. Dis. 10(8) (2016), e0004968.
  23. C. Castillo-Chávez and R.H. Thieme, Asymptotically autonomous epidemic models, in: Mathematical Population Dynamics: Analysis of Heterogeneity, 0. Arimo, D.E. Axelrod, and M. Kimmel (eds.), Wuerz Publishing, Winnipeg, MB, Canada, 1995, pp. 33-50.
  24. S. Cauchemez, M. Besnard, P. Bompard, et al., Association between Zika virus and microcephaly in French Polynesia, 2013-15: a retrospective study, Lancet 387(10033) (2016), 2125-2132.
  25. F.R. Cugola, I.R. Fernandes, F.B. Russo, B.C Freitas, J.L.M. Dias, K.P. Guimaraes, et al., The Brazilian Zika virus strain causes birth defects in experimental models, Nature 534 (2016), 267-271.
  26. M. Darwish, A seroepidemiological survey for bunyaviridae and certain other arboviruses in Pakistan, Trans. R. Soc. Trop. Med. Hyg. 77(4) (1983), 446-450.
  27. G.W. Dick, S.F. Kitchen, and A.J. Haddow, Zika virus. I. isolations and serological specificity, Trans. R. Soc. Trop. Med. Hyg. 46(5) (1952), 509-520.
  28. G.W. Dick, Zika virus. II. pathogenicity and physical properties, Trans. R. Soc. Trop. Med. Hyg. 46(5) (1952), 521-534.
  29. L. Dinh, G. Chowell, K. Mizumoto, and H. Nishiura, Estimating the subcritical transmissibility of the Zika outbreak in the state of Florida, USA, 2016, Theoret. Biol. Med. Modell. 13(1) (2016) 1-7.
  30. M.R. Duffy, Zika virus outbreak on Yap Island, federated states of Micronesia, N. Engl. J. Med. 360(24) (2009), 2536-2543.
  31. M. Ehrhardt and R.E. Mickens, A Nonstandard Finite Difference Scheme for Solving a Zika Virus Model, unpublished manuscript, 2017.
  32. M. Farman, A. Akgl, S. Askar, T. Botmart, A. Ahmad, and H. Ahmad, Modeling and analysis of fractional order Zika model, Virus 3 (2021), 4.
  33. D. Gao, Prevention and control of Zika as a mosquito-borne and sexually transmitted disease: a mathematical modeling analysis, Sci. Rep. 6(28070) (2016), 1-10.
  34. D. Gatherer and A. Kohl, Zika virus: a previously slow pandemic spreads rapidly through the Americas, J. Gen. Virol. 97(2) (2016), 269-273.
  35. C. Gokila and M. Sambath, Modeling and simulations of a Zika virus as a mosquito-borne transmitted disease with environmental fluctuations, Int. J. Nonl. Sci. Numer. Simul. (2021).
  36. A. Haddow, Twelve isolations of Zika virus from Aedes (Stegomyia) Africanus (Theobald) taken in and above a Uganda forest, Bull. World Health Organ. 31(1) (1964), 57-69.
  37. A.D. Haddow, A. J. Schuh, C. Y. Yasuda, et al., Genetic characterization of Zika virus strains: geographic expansion of the Asian line age, PLoS Negl. Trop. Dis. 6(2) (2012), e1477.
  38. B. Hasan, M. Singh, D. Richards, and A. Blicblau, Mathematical modelling of Zika virus as a mosquito-borne and sexually transmitted disease with diffusion effects, Math. Comput. Simulat. 166 (2019), 56-75.
  39. E.B. Hayes, Zika virus outside Africa, Emerg. Infect. Dis. 15(9) (2009), 1347-1350.
  40. J.L. Helmersson, H. Stenlund, A.W. Smith, and J. Rocklö, Vectorial capacity of Aedes Aegypti: effects of temperature and implications for global Dengue epidemic potential, PLoS one 9(3) (2014), 1-10.
  41. S. Ioos, H.P. Mallet, I.L. Goffart, V. Gauthier, T. Cardoso, and M. Herida, Current Zika virus epidemiology and recent epidemics, Medecine et maladies infectieuses 44(7) (2014), 302-307.
  42. R. Isea and K.E. Lonngren, A preliminary mathematical model for the dynamic transmission of Dengue, Chikungunya and Zika, Amer. J. Mod. Phys. Appl. 3(2) (2016), 11-15.
  43. M. Jagan, M.S. deJonge, O. Krylova, and D.J.D. Earn, Fast estimation of time-varying infectious disease transmission rates, PLoS Comput. Biol. 16(9) (2020), e1008124.
  44. V.L.P. Junior, K. Luz, R. Parreira, and P. Ferrinho, Zika virus: a review to clinicians, Acta Médica Portuguesa 28(6) (2015), 760-765.
  45. W.O. Kermack and A.G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. A Math. Phys. Eng. Sci. 115(772) (1927), 700-721.
  46. M. Khalil, A. Am Arafa, and A. Sayed, A variable fractional order network model of Zika virus, J. Fract. Calc. Appl. 9(1) (2018), 204-221.
  47. M.A. Khan, S.W. Shah, S. Ullah, and J.F. Gómez-Aguilar, A dynamical model of asymptomatic carrier Zika virus with optimal control strategies, Nonlinear Analysis: Real World Appl. 50 (2019), 144-170.
  48. M.A. Khan, S. Ullah, and M. Farhan, The dynamics of Zika virus with Caputo fractional derivative, AIMS Math. 4(1) (2019), 134-146.
  49. M.A. Khan, M. Ismail, S. Ullah, and M. Farhan, Fractional order SIR model with generalized incidence rate, AIMS Math. 5(3) (2020), 1856-1880.
  50. A.J. Kucharski, S. Funk, R.M. Eggo, H.-P. Mallet, W.J. Edmunds, and E.J. Nilles, Transmission dynamics of Zika virus in island populations: a modelling analysis of the 2013/14 French Polynesia outbreak, PLoS neglected tropical diseases 10(5) (2016): e0004726.
  51. L. Lambrechts, Impact of daily temperature fluctuations on Dengue virus transmission by Aedes Aegypti, Proc. Natl. Acad. Sci. USA 108(1) (2011), 7460-7465.
  52. E.K. Lee, Y. Liu, and F.H. Pietz, A compartmental model for Zika virus with dynamic human and vector populations, AMIA Annu. Symp. Proc. 2016 (2011), 743-752.
  53. V.M.C. Lormeau, Zika virus, French Polynesia, South Pacific, Emerg. Infect. Dis. 20(6) (2014), 1085-1086.
  54. M.H. Maamar, L. Bouzid, O. Belhamiti, and F.B.M. Belgacem, Stability and numerical study of theoretical model of Zika virus transmission, Int. J. Math. Modell. Numer. Optim. 10(2) (2020), 141-166.
  55. M.H. Maamar, M. Ehrhardt, and L. Tabharit, A nonstandard finite difference scheme for a model of Zika virus transmission, in preparation.
  56. R.W. Malone, J. Homan, M.V. Callahan, et al., Zika virus: medical countermeasure development challenges, PLoS Negl.Trop. Dis. 10(3) (2016), e0004530.
  57. C. Manore, and M. Hyman, Mathematical models for fighting Zika virus, SIAM News 49(4) (2016), 1.
  58. C.A. Manore, R.S. Ostfeld, F.B. Agusto, H. Gaff, and S.L. LaDeau, Defining the risk of Zika and Chikungunya virus transmission in human population centers of the eastern United States, PLoS Neglected Tropical Diseases 11(1) (2017), e0005255.
  59. M. Martcheva, An Introduction to Mathematical Epidemiology, Springer, New York, 2015.
  60. J.P. Messina, Mapping global environmental suitability for Zika virus, elife 5 (2016), e15272.
  61. A.A. Momoh and A. Fügenschuh, Optimal control of intervention strategies and cost effectiveness analysis for a Zika virus model, Oper. Res. Health Care 18 (2018) 99-111.
  62. R.E. Mickens, Applications of Nonstandard Finite Difference Schemes, World Scientific, 2000.
  63. R.E. Mickens, Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition, Numer. Meth. Part. Diff. Eqs. 23(3) (2007), 672-691.
  64. S.C. Mpeshe, N. Nyerere, and S. Sanga, Modeling approach to investigate the dynamics of Zika virus fever: A neglected disease in Africa, Int. J. Adv. Appl. Math. Mech. 4(3) (2017) 14-21.
  65. D. Musso and D.J. Gubler, Zika virus: following the path of Dengue and Chikungunya?, Lancet 386(9990) (2015), 243-244.
  66. D. Musso and D.J. Gubler, Zika virus, Clin. Microbiol. Rev. 29(3) (2016), 487-524.
  67. P.A. Naik, Global dynamics of a fractional-order SIR epidemic model with memory, Int. J. Biomath. 13(8) (2020), 2050071.
  68. P.A. Naik, M. Yavuz, and J. Zu, The role of prostitution on HIV transmission with memory: A modeling approach, Alexandria Engrg. J. 59(4) (2020), 2513-2531.
  69. T.X. Nhan, V.M.C. Lormeau, and D. Musso, Les infections virus zika, Rev. Francoph. des Lab. 2014(467) (2014), 45-52.
  70. H. Nishiura, R. Kinoshita, K. Mizumoto, Y. Yasuda, and K. Nah, Transmission potential of Zika virus infection in the south pacific, Int. J. Infect. Dis. 45 (2016), 95-97.
  71. E. Okyere, S. Olaniyi, and E. Bonyah, Analysis of Zika virus dynamics with sexual transmission route using multiple optimal controls, Scientific African 9 (2020), e00532.
  72. S.J.A.M. Olaniyi, Dynamics of Zika virus model with nonlinear incidence and optimal control strategies, Appl. Math. Inf. Sci. 12(5) (2018), 969-982.
  73. A.M. Oster, Interim guidance for prevention of sexual transmission of Zika virus-United States, 2016, MMWR. Morb. Mortal. Wkly Rep. 65 (2016), 120-121.
  74. PAHO/WHO from Brazil, International Health Regulation (IHR), National Focal Point (NFP), PAHO/WHO, 2 March, 2017.
  75. T.A. Perkins, A.S. Siraj, C.W. Ruktanonchai, M.U. Kraemer, and A.J. Tatem, Model-based projections of Zika virus infections in childbearing women in the Americas, Nat. Microbiol. 1(9) (2016), 16126.
  76. R. Prasad, K. Kumar, and R. Dohare, Caputo fractional order derivative model of Zika virus transmission dynamics, J. Math. Comput. Sci. 2023(28) (2023), 145-157.
  77. R. Rakkiyappan, V.P. Latha, and F.A. Rihan, A fractional-order model for Zika virus infection with multiple delays, Complexity, 2019.
  78. S. Rezapour, H. Mohammadi, and A. Jajarmi, A new mathematical model for Zika virus transmission, Adv. Difference Eqs. 2020(1) (2020), 1-15.
  79. R.G. Sargent, Verification and validation of simulation models, J. Simul. 7(1) (2013), 12-24.
  80. T.W. Scott, Longitudinal studies of Aedes Aegypti (Diptera: Culicidae) in Thailand and Puerto Rico: blood feeding frequency, J. Med. Entomol. 37(1) (2000), 89-101.
  81. P. Shapshak, Global Virology I - Identifying and Investigating Viral Diseases, Springer, New York, 2015.
  82. M.A. Taneco-Hernández and C. Vargas-De-León, Stability and Lyapunov functions for systems with Atangana-Baleanu Caputo derivative: an HIV/AIDS epidemic model, Chaos, Solitons & Fractals 132 (2020), 109586.
  83. Y.A. Terefe, H. Gaff, M. Kamga, and L. van der Mescht, Mathematics of a model for Zika transmission dynamics, Theory Biosci. 137(2) (2018) 209-218.
  84. J. Tolles and T.B. Long, Modeling epidemics with compartmental models, JAMA Guide Stat. Meth. 323(24) (2020), 2515-2516.
  85. S. Treibert, H. Brunner, and M. Ehrhardt, A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics, Math. Biosci. Engrg 19(2) (2022), 1213-1238.
  86. D. Wang, A. Xiao, and J. Zou, Long-time behavior of numerical solutions to nonlinear fractional ODEs. ESAIM: Math. Modell. Numer. Anal. 54(1) (2020), 335-358.
  87. D. Wang and J. Zou, Mittag-Leffler stability of numerical solutions to time fractional ODEs, Numerical Algorithms (2022), 1-35.
  88. F.L.H. Wertheim, P. Horby, and J.P. Woodall, Atlas of Human Infectious Diseases, Wiley-Blackwell, Oxford, 2012.
  89. Y. Xing and Y. Yan, A higher order numerical method for time fractional partial differential equations with nonsmooth data, J. Comput. Phys. 357 (2018), 305-323.
  90. C. Zanluca, First report of autochthonous transmission of Zika virus in Brazil, Inst. Oswaldo Cruz. 110(4) (2015), 569-572.


University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

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