Citation: Zongmin Yue, Fauzi Mohamed Yusof, Sabarina Shafie. Transmission dynamics of Zika virus incorporating harvesting[J]. 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. |