MATHEMATICAL MODELLING ON THE TRANSMISSION DYNAMICS OF ZIKA VIRUS TRANSMISSION DYNAMICS OF ZIKA VIRUS

Main Article Content

Mullai Murugappan
G.Madhan Kumar
Grienggrai Rajchakit
Govindan Vetrivel

Abstract

Zika virus is a mosquito-borne virus that is commonly transmitted by mosquitoes of the Aedes genus. The transmission dynamics of the Zika virus in males, females, and children are comparatively studied. The study aims to analyze and find the population that affects more due to Zika transmission. This paper deals with the non-linear Mathematical model of the dynamics of Zika virus transmission.  The reproductive ratio of the model is calculated to analyze the spread of the Zika virus.  The equilibrium and the stability of the model are found and analyzed analytically. Numerical simulation is carried out to support the analytical results and to estimate the most affecting population in different equilibria.


 


 


(Manuscript received: 23 June 2023 | Accepted: 14 August 2023 | Published: 30 September 2023)

Article Details

How to Cite
Murugappan, M., G, M. K., Grienggrai, R., & Govindan, V. (2023). MATHEMATICAL MODELLING ON THE TRANSMISSION DYNAMICS OF ZIKA VIRUS: TRANSMISSION DYNAMICS OF ZIKA VIRUS. International Journal on Robotics, Automation and Sciences, 5(2), 79–84. https://doi.org/10.33093/ijoras.2023.5.2.9
Section
Articles
Author Biographies

G.Madhan Kumar, Department of Mathematics, Alagappa University (India)

Research Scholar, Alagappa University, Karaikudi

Grienggrai Rajchakit, Department of Mathematics, Faculty of Science, Maejo University (Thailand)

Associate Professor, Department of Mathematics, Maejo University, Thailand.

Govindan Vetrivel, Department of Mathematics, Alagappa University (India)

Research Scholar, Alagappa University, Karaikudi.

References

F.B. Agusto, S. Bewick, W.F. Fagan, “Mathematical model of Zika virus with vertical transmission”, Infectious Disease Modelling, vol. 2, no. 2, pp. 244-267, May 2017.

Ahmed Alshehri and Miled El hajji,” Mathematical study for Zika virus transmission with general incidence rate”, AIMS Mathematics, vol. 7, no. 4, pp. 7117-7142, 2022.

P.Brasil, et al., “Zika virus infection in Pregnant women in Rio de Janeiro”, The new England Journal of medicine, vol. 375, no. 24, pp. 2321-2334, Dec 2016.

Brian D Foy, Kevin C Kobylinski, Joy L Chilson Foy et al., “Probable non-vector-borne transmission of Zika virus, Colorado, USA”, Emerg Infect Dis, vol. 17, no. 5, pp. 1-7, May 2011.

Susan L. Hill, Kate Russell et al., “Transmission of Zika Virus Through Sexual Contact with Travelers to Areas of Ongoing Transmission— Continental United States”, Morbidity and Mortality Weekly Report, ePub: 26 February 2016.

Mahmoud A. Ibrahim, Attila Denes, “A Mathematical Model for Zika Virus Infection and Microcephaly Risk Considering Sexual and Vertical Transmission”, Axioms, 12, 263, pp. 1-25, 2023.

Juan Carlos Jamboos, et al., “Simulation model to the Zika virus considering Asymptomatic population”, Open Journal of modelling and simulation, vol. 6, no. 1, pp. 1-12, Jan 2018.

Istvan Z. Kiss, Joel C. Miller et al., “Mathematics of epidemics on networks: From Exact to Approximate Models”. Springer Textbook, 2017.

Munsur Rahman, Kidist Bekele-Maxwell, LeAnna L. Cates, H.T. Banks, Naveen K. Vaidya, “Modeling Zika Virus Transmission Dynamics: Parameter Estimates, Disease Characteristics, and Prevention”, Scientific Reports, 9:10575, pp. 1-13, 2019.

D Musso, T Nhan, E Robin, C Roche, D Bierlaire, K Zisou et al., “Potential for Zika virus transmission through blood transfusion demonstrated during an outbreak in French Polynesia”, Euro Surveill, 19(14):20761, pp. 1-3, Apr 2014.

D Musso, C Roche, E Robin, T Nhan, A Teissier, VM Cao-Lormeau, “Potential sexual transmission of Zika virus”, Emerg Infect Dis, Feb;21(2):359-61, Feb 2015.

Joel C. Miller, “Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes”, Infectious Disease Modelling, vol. 2, no. 1, pp. 35-55, Feb 2017.

AS Oliveira Melo, G Malinger, R Ximenes, P O Szejnfeld, S Alves Sampaio, AM Bispo de Filippis, “Zika virus intrauterine infection causes fetal brain abnormality and microcephaly: tip of the iceberg?” Ultrasound Obstet Gynecol, 47(1): 6-7, Jan 2016.

M.D. Oscar Pacheco, M.S. Mauricio Beltran, Christina A. Nelson et al., “Zika virus disease in Colombia — preliminary report”, N Engl J Med, Aug 2020.

Parinya Suparit, Anuwat Wiratsudakul, Charin Modchang, “A mathematical model for Zika virus transmission dynamics with a time-dependent mosquito biting rate”, 15:11, pp. 1-11, 2018.

Ravins Dohare, Manoj kumar, Shweta Sankhwar, Narender Kumar, Surendra Kumar Sagar, Jugal Kishore, “SIR-SI Mathematical Model for Zika Virus Progression Dynamics in India: A Case Study”, vol. 53, no. 2, pp. 100-104, 2021.

Shahram Rezapour, Hakimeh Mohammadi, Amin Jajarmi, “A new mathematical model for zika virus transmission”, Advances in Difference Equations, 589, pp. 1-15, 2020.

Sudhanshu Kumar Biswas, Uttam Ghosh, Susmita Sarkar, “Mathematical model of zika virus dynamics with vector control and sensitivity analysis”, Infectious Disease Modelling, 5, pp. 23-41, 2020.

Sudhanshu Kumar Biswas, Uttam Ghosh, Susmita Sarkar, “A mathematical model of Zika virus transmission with saturated incidence and optimal control: A case study of 2016 zika outbreak in Puerto Rico”, International Journal of Modelling and Simulation, 2023.

G Venturi, L Zammarchi, C Fortuna, ME Remoli et al., “An autochthonous case of Zika due to possible sexual transmission, Florence, Italy, 2014”, Euro Surveill, vol. 21, no. 8, 2016.

N Wikan et al., “Immunological evidence of Zika virus transmission in Thailand”, Asian Pac J Trop Med, vol. 9, no. 2, pp. 141–144, Feb 2016.