Transmission dynamics of Zika virus incorporating harvesting

Zongmin Yue; Fauzi Mohamed Yusof; Sabarina Shafie; Zongmin Yue; Fauzi Mohamed Yusof; Sabarina Shafie

doi:10.3934/mbe.2020327

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 6181-6202. doi: 10.3934/mbe.2020327

Previous Article Next Article

Research article Special Issues

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: 22 August 2020 Accepted: 07 September 2020 Published: 14 September 2020

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.

Keywords:

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

Related Papers:

[1]	Mitchell Ratner, Chih-Chieh (Jason) Chiu . Portfolio Effects of VIX Futures Index. Quantitative Finance and Economics, 2017, 1(3): 288-299. doi: 10.3934/QFE.2017.3.288
[2]	Akash Deep . Advanced financial market forecasting: integrating Monte Carlo simulations with ensemble Machine Learning models. Quantitative Finance and Economics, 2024, 8(2): 286-314. doi: 10.3934/QFE.2024011
[3]	Lucjan T. Orlowski, Monika Sywak . Wavering interactions between commodity futures prices and us dollar exchange rates. Quantitative Finance and Economics, 2019, 3(2): 221-243. doi: 10.3934/QFE.2019.2.221
[4]	Gabriel Frahm . How often is the financial market going to collapse?. Quantitative Finance and Economics, 2018, 2(3): 590-614. doi: 10.3934/QFE.2018.3.590
[5]	Etti G. Baranoff, Patrick Brockett, Thomas W. Sager, Bo Shi . Was the U.S. life insurance industry in danger of systemic risk by using derivative hedging prior to the 2008 financial crisis?. Quantitative Finance and Economics, 2019, 3(1): 145-164. doi: 10.3934/QFE.2019.1.145
[6]	Cunyi Yang, Li Chen, Bin Mo . The spillover effect of international monetary policy on China's financial market. Quantitative Finance and Economics, 2023, 7(4): 508-537. doi: 10.3934/QFE.2023026
[7]	Dimitra Loukia Kolia, Simeon Papadopoulos . The levels of bank capital, risk and efficiency in the Eurozone and the U.S. in the aftermath of the financial crisis. Quantitative Finance and Economics, 2020, 4(1): 66-90. doi: 10.3934/QFE.2020004
[8]	Andrea Ferrario, Massimo Guidolin, Manuela Pedio . Comparing in- and out-of-sample approaches to variance decomposition-based estimates of network connectedness an application to the Italian banking system. Quantitative Finance and Economics, 2018, 2(3): 661-701. doi: 10.3934/QFE.2018.3.661
[9]	Chen Li, Xiaohu Li . Stochastic arrangement increasing risks in financial engineering and actuarial science – a review. Quantitative Finance and Economics, 2018, 2(1): 675-701. doi: 10.3934/QFE.2018.1.190
[10]	Jyh-Horng Lin, Shi Chen, Jeng-Yan Tsai . How does soft information about small business lending affect bank efficiency under capital regulation?. Quantitative Finance and Economics, 2019, 3(1): 53-74. doi: 10.3934/QFE.2019.1.53

Abstract

References

[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.

This article has been cited by:

1.	N.I. Yashina, O.I. Kashina, S.S. Petrov, N.N. Pronchatova-Rubtsova, Developing the methodology of early diagnosis of financial crises using a system of signaling economic indicators, 2020, 13, 20734484, 362, 10.24891/fa.13.4.362
2.	Yue Liu, Hao Dong, Pierre Failler, The Oil Market Reactions to OPEC’s Announcements, 2019, 12, 1996-1073, 3238, 10.3390/en12173238
3.	Lean Yu, Xiaowen Huang, Hang Yin, Can machine learning paradigm improve attribute noise problem in credit risk classification?, 2020, 70, 10590560, 440, 10.1016/j.iref.2020.08.016
4.	Luís Almeida, Francisco Sousa, Determinants of bank profitability in Portugal: Insights from a period of sectoral transformation, 2025, 9, 2573-0134, 425, 10.3934/QFE.2025014

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)