
Mathematical Biosciences and Engineering, 2020, 17(5): 61816202. doi: 10.3934/mbe.2020327
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
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
Received: , Accepted: , Published:
Special Issues: Mathematical modeling and analysis of social and ecological determinants for the dynamics of infectious diseases and public health policies
References
1. D. I. H. Simpson, Zika virus infection in man, Trans. R. Soc. Trop. Med. Hyg., 58 (1964), 335337.
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), 569572.
4. M. A. Khan, S. Ullah, M. Farhan, The dynamics of Zika virus with Caputo fractional derivative, AIMS Math., 4 (2019), 134146.
5. W. O. k. G. McKendrick, A contribution to the mathematical theory of epidemics. I., Proc. R. Soc. London, 115 (1927), 700721.
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), 94122.
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 20132014 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), 89298941.
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/calcinit/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), 108118.
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), 341344.
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 ecoepidemiological systemA theoretical study, Math. Biosci., 217 (2009), 134144.
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), 935940.
17. K. P. Das, A study of harvesting in a predatorprey model with disease in both populations, Mathe. Methods Appl. Sci., 39 (2016), 28532870.
18. E. Bonyah, M. A. Khan, K. O. Okosun, S. Islam, A theoretical model for Zika virus transmission, PLOS ONE, 12 (2017), 118.
19. P. V. D. Driessche, J. Watmough, Reproduction numbers and subthreshold endemic equilibrium for compartmental models of disease transmission, Math. Biosci., 180 (2002), 2948.
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. NedjatiGilani, C. A. Donnelly, M. G. Basáñez, et al., Countering the Zika epidemic in Latin America, Science, 353 (2016), 353354.
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), 174191.
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)