SIR-SI Mathematical Model for Zika Virus Progression Dynamics in India: A Case Study
Abstract
Viral diseases are very hazardous for humanity because in the case of most viral diseases, drugs are not effective. At present, the whole world is living with the fear of COVID-19. From time to time, several viral diseases have been troubling human life. In this article, we have tried to capture the progression dynamics of Zika Virus (ZIKV) infection in the Indian scenario. A constructed model is based on compartment modelling. In the model, Susceptible-Infected-Recovered (SIR) structure is used for the human population and Susceptible-Infected (SI) structure is used for mosquito population. The value of the basic reproduction number (R0) is computed 0.36 at baseline values of parameters involved in the model. The lower value of R0 suggests that infection was unable to spread in the human population. Sensitive analysis for R0 revealed that the most accountable parameter in the spread of infection was mosquito biting rate. The modelling technique might be useful for other diseases also.
How to cite this article:
Dohare R, Kumar M, Sankhwar S, Kumar N, Sagar SK, Kishore J. SIR-SI Mathematical Model for Zika Virus Progression Dynamics in India: A Case Study. J Commun Dis. 2021; 53(2): 100-104.
DOI: https://doi.org/10.24321/0019.5138.202132
References
Pan American Health Organization/ World Health Organization [Internet]. Zika; 2016 Apr 6[cited 2017
Nov 30]. Available from: http://www.paho.org/hq/index.php?option=com_content&view=article&id=1
%3Azika-virus-infection&catid=8424%3Acontents&Itemid=41688&lang=en
Cauchemez S, Besnard M, Bompard P, Dub T, Guillemette-Artur P, Eyrolle-Guignot D, Salje H, Van
Kerkhove MD, Abadie V, Garel C, Fontanet A, Mallet HP. Association between Zika virus and microcephaly
in French Polynesia, 2013-15: a retrospective study. Lancet. 2016;387(10033):2125-32. [Pubmed] [Google
Scholar]
Centers for Disease Control and Prevention [Internet]. About Zika; 2014 Nov 5 [cited 2017 Sep 28]. Available
from: https://www.cdc.gov/zika/about/index.html
Cao-Lormeau VM, Blake A, Mons S, Lastère S, Roche C,Vanhomwegen J, Dub T, Baudouin L, Teissier A, Larre
P, Vial AL, Decam C, Choumet V, Halstead SK, Willison HJ, Musset L, Manuguerra JC, Despres P, Fournier E,
Mallet HP, Musso D, Fontanet A, Neil J, Ghawché F. Guillain-Barré Syndrome outbreak associated with
Zika virus infection in French Polynesia: a case-control study. Lancet. 2016;387(10027):1531-9. [PubMed]
[Google Scholar]
Kumar N, Abdullah M, Faizan MI, Ahmed A, Alsenaidy HA, Dohare R, Parveen S. Progression dynamics of
Zika fever outbreak in El Salvador during 2015–2016: a mathematical modeling approach. Future Virol.
;12(5):271-81. [Google Scholar]
Andraud M, Hens N, Marais C, Beutels P. Dynamic Epidemiological Models for Dengue Transmission: A
Systematic Review of Structural Approaches. PLoS One. 2012;7(11):e49085. [PubMed] [Google Scholar]
Medeiros LC, Castilho CA, Braga C, de Souza WV, Regis L, Monteiro AM. Modeling the Dynamic Transmission
of Dengue Fever: Investigating Disease Persistence. PLoS Negl Trop Dis. 2011;5(1):e942. [PubMed] [Google
Scholar]
Chikaki E, Ishikawa H. A dengue transmission model in Thailand considering sequential infections with all
four serotypes. J Infect Dev Ctries. 2009;3(9):711-22. [PubMed] [Google Scholar]
World Health Organization [Internet]. Zika virus infection – India; [cited 2021 Jul 08]. Available from:
https://www.who.int/news-room/fact-sheets/detail/zika-virus
Diekmann O, Heesterbeek JA, Metz JA. On the definition and the computation of the basic reproduction ratio
Ro in models for infectious diseases in heterogeneous populations. J Math Biol. 1990;28(4):365-82. [PubMed]
[Google Scholar]
Derrick, N.R. and Grossman, S.L. Differential Equation with applications. Addison Wesley Publishing Company,
Inc. Philippines (1976).
Copyright (c) 2021 Journal of Communicable Diseases (E-ISSN: 2581-351X & P-ISSN: 0019-5138)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
