SIR-SI Mathematical Model for Zika Virus Progression Dynamics in India: A Case Study

  • Ravins Dohare Centre for Interdisciplinary Research in Basic Sciences, Jamia Millia Islamia, Jamia Nagar, New Delhi, India.
  • Manoj Kumar Centre for Economic Studies and Planning, Jawaharlal Nehru University, India.
  • Shweta Sankhwar Department of Computer Science, Maitreyi College (University of Delhi), New Delhi, India.
  • Narender Kumar Department of Mathematics, Gargi College, University of Delhi, India.
  • Surendra Kumar Sagar Department of Zoology, Swami Shraddhanand College (University of Delhi), Delhi, India.
  • Jugal Kishore Department-Community Medicine, VMMC & Safdarjung Hospital (Ministry of Health & Family Welfare) New Delhi, India
Keywords: Zika Virus Infection, Disease-free Equilibrium, Basic Reproduction Number, Numerical Simulation


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.



Pan American Health Organization/ World Health Organization [Internet]. Zika; 2016 Apr 6[cited 2017

Nov 30]. Available from:


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


Centers for Disease Control and Prevention [Internet]. About Zika; 2014 Nov 5 [cited 2017 Sep 28]. Available


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


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:

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).