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Transmission dynamics of Zika virus incorporating harvesting

1 Faculty of Science and Mathematics, Sultan Idris Education University, Tanjong Malim Perak 35900, Malaysia
2 School of Arts and sciences, Shaanxi University of Science and Technology, Xi’an 710021, China

Special Issues: Mathematical modeling and analysis of social and ecological determinants for the dynamics of infectious diseases and public health policies

In this paper, we establish a ZIKV model and investigate the transmission dynamics of ZIKV with two types of harvesting: proportional harvesting and constant harvesting, and give the stability of the steady states of both disease-free and endemic equilibrium, analyze the effect of harvesting on ZIKV transmission dynamics via numerical simulation. We find that proportional harvesting strategy can eliminate the virus when the basic reproduction number R0 is less than 1, but the constant harvesting strategy may control the virus whether the basic reproduction number is less than 1 or not. Epidemiologically, we find that increasing harvesting may stimulate an increase in the number of virus infections at some point, and harvesting can postpone the peak of disease transmission with the mortality of mosquito increasing. The results can provide us with some useful control strategies to regulate ZIKV dynamics.
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Keywords ZIKV; harvesting; equilibrium; stability; numerical simulation

Citation: Zongmin Yue, Fauzi Mohamed Yusof, Sabarina Shafie. Transmission dynamics of Zika virus incorporating harvesting. Mathematical Biosciences and Engineering, 2020, 17(5): 6181-6202. doi: 10.3934/mbe.2020327


  • 1. D. I. H. Simpson, Zika virus infection in man, Trans. R. Soc. Trop. Med. Hyg., 58 (1964), 335-337.
  • 2. J. T. Beaver, N. Lelutiu, R. Habib, I. Skountzou, Evolution of Two Major Zika Virus Lineages: Implications for Pathology, Immune Response, and Vaccine Development, Front. Immunol., 9 (2018), 1640.
  • 3. C. Zanluca, V. C. Melo, A. L. Mosimann, C. N. Santos, K. Luz, First report of autochthonous transmission of Zika virus in Brazil, Mem. Inst. Oswaldo Cruz, 110 (2015), 569-572.
  • 4. M. A. Khan, S. Ullah, M. Farhan, The dynamics of Zika virus with Caputo fractional derivative, AIMS Math., 4 (2019), 134-146.
  • 5. W. O. k. G. McKendrick, A contribution to the mathematical theory of epidemics. I., Proc. R. Soc. London, 115 (1927), 700-721.
  • 6. W. O. k. G. McKendrick, Contributions to the mathematical theory of epidemics. III.-Further studies of the problem of endemicity, Proc. R. Soc. London, 141 (1933), 94-122.
  • 7. S. Funk, A. J. Kucharski, A. Camacho, R. M. Eggo, L. Yakob, L. M. Murray, et al., Comparative analysis of dengue and Zika outbreaks reveals differences by setting and virus, PLoS Neglected Trop. Dis., 10 (2019), e0005173.
  • 8. A. J. Kucharski, S. Funk, R. M. Eggo, H. P. Mallet, W. J. Edmunds, et al., Transmission dynamics of Zika virus in island populations: A modelling analysis of the 2013-2014 French polynesia outbreak, PLoS Neglected Trop. Dis., 10 (2016), e0004726
  • 9. F. Ndaïrou, I. Area, J. J. Nieto, C. J. Silva, D. F. M. Torres, Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil, Math. Methods Appl. Sci., 41 (2018), 8929-8941.
  • 10. P. Suparit, A. Wiratsudakul, C. Modchang, A mathematical model for Zika virus transmission dynamics with a time dependent mosquito biting rate, Theor. Biol. Med. Modell., 15 (2018), 11.
  • 11. R. Miner, F. Wicklin, Modeling population growth: harvesting, 1996. Available from: http://www.geom.uiuc.edu/education/calc-init/population/harvest.html.
  • 12. P. K. Stoddard, Managing aedes aegypti populations in the first zika transmission zones in the continental united states, Acta Tropica, 187 (2018), 108-118.
  • 13. C. Y. Wang, H. J. Teng, S. J. Lee, C. Lin, J. W. Wu, H. S. Wu, Efficacy of various larvicides against aedes aegypti immatures in the laboratory, Jpn. J. Infect. Dis., 66 (2013), 341-344.
  • 14. A. J. Cornel, J. Holeman, C. C. Nieman, Y. Lee, C. Smith, M. Amorino, et al., Surveillance, insecticide resistance and control of an invasive Aedes aegypti (Diptera: Culicidae) population in California, F1000 Res., 5 (2016), 194.
  • 15. N. Bairagi, S. Chaudhuri, J. Chattopadhyay, Harvesting as a disease control measure in an eco-epidemiological system-A theoretical study, Math. Biosci., 217 (2009), 134-144.
  • 16. F. M. Yusof, A.I.B. MD. Ismail, N. M. Ali, Modeling Population Harvesting of Rodents for the control of Hantavirus Infection, Sains Malays., 39 (2010), 935-940.
  • 17. K. P. Das, A study of harvesting in a predator-prey model with disease in both populations, Mathe. Methods Appl. Sci., 39 (2016), 2853-2870.
  • 18. E. Bonyah, M. A. Khan, K. O. Okosun, S. Islam, A theoretical model for Zika virus transmission, PLOS ONE, 12 (2017), 1-18.
  • 19. P. V. D. Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibrium for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
  • 20. Z. E. Ma, Y. C. Zhou, Qualitative and Stability methods for ordinary differential equations, Science Press, (2001).
  • 21. N. M. Ferguson, Z. M. Cucunubá, I. Dorigatti, G. L. Nedjati-Gilani, C. A. Donnelly, M. G. Basáñez, et al., Countering the Zika epidemic in Latin America, Science, 353 (2016), 353-354.
  • 22. C. A. Manore, K. S. Hickmann, S. Xu, H. J. Wearing, J. M. Hyman, Comparing dengue and chikungunya emergence and endemic transmission in A. aegypti and A. albopictus, J. Theor. Biol., 356 (2014), 174-191.


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