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A mathematical model to study the 2014–2015 large-scale dengue epidemics in Kaohsiung and Tainan cities in Taiwan, China

1 Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
2 School of Nursing, Hong Kong Polytechnic University, Hong Kong, China
3 Complex System Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
4 Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006, Shanxi, China
5 Key Laboratory of Computational Intelligence and Chinese Information, Processing of Ministry of Education, Taiyuan 030006, China

Special Issues: Mathematical Modeling of Mosquito-Borne Diseases

Dengue virus (DENV) infection is endemic in many places of the tropical and subtropical regions, which poses serious public health threat globally. We develop and analyze a mathematical model to study the transmission dynamics of the dengue epidemics. Our qualitative analyzes show that the model has two equilibria, namely the disease-free equilibrium (DFE) which is locally asymp- totically stable when the basic reproduction number ($Ro$ ) is less than one and unstable if $Ro$ > 1, and endemic equilibrium (EE) which is globally asymp-totically stable when $Ro$ > 1. Further analyzes reveals that the model exhibit the phenomena of backward bifurcation (BB) (a situation where a stable DFE co-exists with a stable EE even when the $Ro$ < 1), which makes the disease control more diffi-cult. The model is applied to the real dengue epidemic data in Kaohsiung and Tainan cities in Taiwan, China to evaluate the fitting performance. We propose two reconstruction approaches to estimate the time-dependent $Ro$ , and we find a consistent fitting results and equivalent goodness-of-fit. Our findings highlight the similarity of the dengue outbreaks in the two cities. We find that despite the proximity in Kaohsiung and Tainan cities, the estimated transmission rates are neither completely synchronized, nor periodically in-phase perfectly in the two cities. We also show the time lags between the seasonal waves in the two cities likely occurred. It is further shown via sensitivity analysis result that proper sanitation of the mosquito breeding sites and avoiding the mosquito bites are the key control measures to future dengue outbreaks in Taiwan.
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References

1. H. H. G. Silva and I. G. Silva, Influence of eggs quiescence period on the aedes aegypti (Linnaeus, 1762) (diptera, culicidae) life cycle at laboratory conditions, Rev. Soc. Bras. Med. Trop., 32 (1999), 349–355.

2. C. J. McMeniman and S. L. O'Neill, A virulent wolbachia infection decreases the viability of the dengue vector aedes aegypti during periods of embryonic quiescence, PLoS Negl. Trop. Dis., 4 (2010), e748.

3. H. M. Yang and C. P. Ferreira, Assessing the effects of vector control on dengue transmission,Appl. Math. Comput., 198 (2008), 401–413.

4. H. M. Yang, M. L. G. Macoris, K. C. Galvani, et al., Follow up estimation of aedes aegypti entomological parameters and mathematical modellings. Biosyst., 103 (2011), 360–371.

5. H. M. Yang, Assessing the influence of quiescence eggs on the dynamics of mosquito aedes ae- gypti, Appl. Math., 5 (2014), 2696–2711.

6. S. M. Garba, A. B. Gumel and M. R. A. Bukar, Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215 (2008), 11–25.

7. K. S. Vannice, A. Durbin and J. Hombach, Status of vaccine research and development of vaccines for dengue, Vaccine, 34 (2016), 2934–2938.

8. World Health Organization, Dengue control, 2017. Available from: http://www.who.int/denguecontrol/human/en/.

9. S. Sang, S. Gu, P. Bi, et al., Predicting unprecedented dengue outbreak using imported cases and climatic factors in guangzhou, PLoS Negl. Trop. Dis., 9 (2014), e0003808.

10. R. M. Lana, T. G. Carneiro, N. A. Honorio, et al., Seasonal and nonseasonal dynamics of aedes aegypti in Rio de Janeiro, Brazil: fitting mathematical models to trap data, Acta Tropic., 129 (2014), 25–32.

11. E. P. Pliego, J. Velazquez-Castro and A. F. Collar, Seasonality on the life cycle of aedes aegypti mosquito and its statistical relation with dengue outbreaks, Appl. Math. Model., 50 (2017), 484–496.

12. K. O. Okuneye, J. X. Valesco-Hernandez and A. B. Gumel, The "unholy" chikungunya-dengue- zika trinity: a theoretical analysis, J. Biol. Syst., 25 (2017), 587–603.

13. D. Gao, Y. Lou, D. He, et al., Prevention and control of zika as a mosquito-borne and sexually transmitted disease: a mathematical modeling analysis, Sci. Rep., 6 (2016), 28070.

14. S. Zhao, L. Stone, D. Gao, et al., Modelling the large-scale yellow fever outbreak in Luanda, Angola, and the impact of vaccination, PLoS Negl. Trop. Dis., 12 (2018), e0006158.

15. P. Guo, T. Liu, Q. Zhang, et al., Developing a dengue forecast model using machine learning: a case study in China, PLoS Negl. Trop. Dis., 11 (2017), e0005973.

16. T. P. O. Evans and S. R. Bishop, A spatial model with pulsed releases to compare strategies for the sterile insect technique applied to the mosquito Aedes aegypti, Math. Biosci., 254 (2014), 6–27.

17. R. R. Mahale, A. Mehta, A. K. Shankar, et al., Delayed subdural hematoma after recovery from dengue shock syndrome, J. Neurosci. Rural Pract., 7 (2016), 323–324.

18. D. J. Gubler, E. E. Ooi, S. G. Vasudevan, et al., Dengue and dengue hemorrhagic fever, 2nd ed. Wallingford, UK: CAB International, 2014.

19. S. F. Wang, W. H. Wang, K. Chang, et al., Severe dengue fever outbreak in Taiwan, Am. J. Trop. Med. Hyg., 94 (2016), 193–197.

20. M. Chan and M. A. Johansson, The incubation periods of dengue viruses, PLoS One, 7 (2012), e50972.

21. C. A. Manore, K. S. Hickman, S. Xu, et al., Comparing dengue and chikungunya emergence and endemic transmission in A. egypti and A.albopictus, J. Theor. Bio., 356 (2014), 174–191.

22. Sanofi Pasteur, First Dengue Vaccine Approved in More than 10 Countries by Sanofi Pasteur, 2019. Available from: https://www.sanofipasteur.com/en/.

23. World Health Organization, Updated Questions and Answers related to information presented in the Sanofi Pasteur press release on 30 November 2017 with regards to the dengue vaccine Deng-vaxia, 2019. Available from: https://www.who.int/immunization/diseases/dengue/q_and_a_dengue_vaccine_dengvaxia/en/.

24. H. M. Yang, M. L. G. Macoris, K. C. Galvani, et al., Assessing the effects of temperature on the population of Aedes aegypti, the vector of dengue, Epidemiol. Infect., 137 (2009), 1188–1202.

25. H. M. Yang, M. L. G. Macoris, K. C. Galvani, et al., Assessing the effects of temperature on dengue transmission, Epidemiol. Infect., 137 (2009), 1179–1187.

26. A. B. Gumel, Causes of backward bifurcations in some epidemiological models, J. Math. Anal. Appl., 395 (2012), 355–365.

27. K. Okuneye and A. B. Gumel, Analysis of a temperature- and rainfall-dependent model for malaria transmission dynamics, Mathe. Biosci., 287 (2017), 72–92.

28. N. Hussaini, K. Okuneye and A. B. Gumel, Mathematical analysis of a model for zoonotic visceral leishmaniasis, Infect. Dis. Model., 2 (2017), 455–474.

29. S.Usaini, U.T.MustaphaandS.M.Sabiu, Modellingscholasticunderachievementasacontagious disease, Math. Meth. Appl. Sci., 41 (2018), 8603–8612.

30. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equi-libria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.

31. T. P. Endy, S. Chunsuttiwat, A. Nisalak, et al., Epidemiology of inapparent and symptomatic acute dengue virus infection: a prospective study of primary school children in Kamphaeng Phet, Thailand, Amer. J. Epi., 156 (2002), 40–51.

32. M. J. P. Poirier, D. M. Moss, K. R. Feeser, et al., Measuring Haitian children's exposure to chikun-gunya, dengue and malaria, Bull World Health Organ., 94 (2016), 817–825.

33. C. H. Chen, Y. C. Huang and K. C. Kuo, Clinical features and dynamic ordinary laboratory tests differentiating dengue fever from other febrile illnesses in children, J. Microb. Immunol. Infect.,51 (2018), 614–620.

34. S. Zhao, Y. Lou, A. P. Chiu, et al., Modelling the skip-and-resurgence of Japanese encephalitis epidemics in Hong Kong, J. Theor. Biol., 454 (2018), 1–10.

35. Y. Xiao, S. Tang and J. Wu, Media impact switching surface during an infectious disease outbreak,Scient. Rep., 5 (2015), 7838.

36. D. L. Smith, K. E. Battle, S. I. Hay, et al., Ross, Macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens, PLoS Pathog., 8 (2012), e1002588.

37. Q. Lin, Z. Lin, A. P. Y. Chiu, et al., Seasonality of influenza A(H7N9) virus in China -fitting simple epidemic models to human cases, PLoS One, 11 (2016), e0151333.

38. C. Breto, D. He, E. L. Ionides , et al., Time series analysis via mechanistic models, Ann. Appl. Stat., 3 (2009), 319–348.

39. The website of R package "pomp": statistical inference for partially-observed Markov processes, 2018. Available from: https://kingaa.github.io/pomp/.

40. D. He, R. Lui, L. Wang, et al., Global Spatio-temporal Patterns of influenza in the post-pandemic era, Sci Rep., 5 (2015), 11013.

41. E. L. Ionides, C. Breto and A. A. King, Inference for nonlinear dynamical systems, Proc. Natl. Acad. Sci., 103 (2006), 18438–18443.

42. E. L. Ionides, A. Bhadra, Y. Atchade, et al., Iterated filtering, Ann. Stat., 39 (2011), 1776–1802.

43. D. J. Earn, D. He, M. B. Loeb, et al., Effects of school closure on incidence of pandemic influenza in Alberta, Canada, Ann. Intern. Med., 156 (2012), 173–181.

44. A. Camacho, S. Ballesteros, A. L. Graham, et al., Explaining rapid reinfections in multiple-wave influenza outbreaks: Tristan da Cunha 1971 epidemic as a case study, Proc. Biol. Sci., 278 (2011), 3635–3643.

45. D. He, J. Dushoff, T. Day, et al., Mechanistic modelling of the three waves of the 1918 influenza pandemic, Theory Ecol., 4 (2011), 283–288.

46. D. He, E. L. Ionides and A. A. King, Plug-and-play inference for disease dynamics: measles in large and small populations as a case study, J. R. Soc. Interf., 7 (2010), 271–283.

47. D. He, D. Gao, Y. Lou, et al., A comparison study of zika virus outbreaks in French Polynesia, Colombia and the state of Bahia in Brazil, Sci. Rep., 7 (2017), 273.

48. S. Zhao, S. S. Musa, J. Qin , et al., Phase-shifting of the transmissibility of macrolide-sensitive and resistant Mycoplasma pneumoniae epidemics in Hong Kong, from 2015 to 2018, Int. J. Infect. Dis., 81 (2019), 251–253.

49. Taiwan National Infectious Disease Statistics System, Dengue, 2018. Available from: https://nidss.cdc.gov.tw/en/Default.aspx?op=4.

50. C. Yang, X. Wang, D. Gao , et al., Impact of awareness programs on cholera dynamics: two modeling approaches, Bull. Math. Biol., 79 (2017), 2109–2131.

51. G. Sun, J. Xie, S. Huang, et al., Transmission dynamics of cholera: mathematical modeling and control strategies, Commun. Non. Sci. Numer. Simulat., 45 (2017), 235–244.

52. J. P. LaSalle, The stability of dynamical systems, Regional Conference Series in Applied Mathe-matics, Soceity for industrial and Applied Mathematics, Philadelphia, 1976.

53. D. S. Shepard, Y. A. Halasa, B. K. Tyagi, et al., Economic and disease burden of dengue illness in India, Am. J. Trop. Med. Hyg., 91 (2014), 1235–1242.

54. N. T. Toan, S. Rossi, G. Prisco, et al., Dengue epidemiology in selected endemic countries: factors influencing expansion factors as estimates of underreporting, Trop. Med. Int. Health., 20 (2015), 840–863.

55. E. Sarti, M. L'Azou, M. Mercado, et al., A comparative study on active and passive epidemio-logical surveillance for dengue in five countries of Latin America, Int. J. Infect. Dis., 44 (2016), 44–49.

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