Impact of early treatment programs on Swine flu infection with optimal controls: Mathematical model

Document Type : Research Paper


1 Govt. Model Science college Gwalior (M.P.)

2 Department of Mathematics, SOS, ITM University Gwalior (M.P.)

3 S. M. S. Govt Model Science College, Gwalior 474010, MP, India


This manuscript focuses on the impact of early treatment programs on swine flu disease transmission among the population. In this manuscript, a nonlinear Susceptible-Exposed-Infected-Recovered (SEIR) model with early Treatment programs are developed to examine the transmission dynamics of Swine flu infection with the help of the system of ordinary differential equations. The characteristics of the model are investigated by the basic reproduction number. We analyzed that the model exhibits using stability theory of differential equations, the disease-free equilibrium is linearly stable for R01. Also, conditions for non-linear stability are derived. Sensitivity indices for basic reproduction and also optimal control measures for swine flu are obtained. Further, numerical simulation for the model is supported by relevant graphs.


[1] Swine influenza, The Merck veterinary manual 2008, ISBN 1-4421-6742-4, Retrieved April 30, ( 2009),
[2] A. Ramirez, A.W. Capuano, D.A. Wellman, K.A. Lesher, S.F. Setterquist and G.C. Gray, Preventing zoonotic
influenza virus infection, Emerg Infect Dis. 12(6) (2006) 996—1000.
[3] Pandemic (H1N1) 2009, Emergencies preparedness, response,[4] Antiviral drugs and Swine influenza. centers for disease control, Retrieved 2009-04-27,
[5] FDA authorizes emergency use of influenza medicines, diagnostic test in response to Swine Flu outbreak in
humans, FDA News April 27, (2009).
[6] N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameter in the spread of malaria through
the sensitivity analysis of mathematical model, Depart. Public Health Epidem. 70 (2008) 1272–1296.
[7] O.P. Misra and D.K. Mishra, Spread and control of influenza in two groups: A model, Appl. Math. Comput. 219
(2013) 7982–7996.
[8] A.K. Srivastav and M. Ghosh, Modeling and analysis of the symptomatic and asymptomatic infections of swine
flu with optimal control, Model. Earth Syst. Environ, 2:177 (2016), DOI: 10.1007/s40808-016-0222-7.
[9] S. M. A. Rahman, N. K. Vaidya and X. Zou, Impact of early treatment programs on HIV epidemics: an immunitybased mathematical model, Math. Biosci. (2016), DOI: 10.1016/j.mbs.2016.07.009.[10] M. Kharis and R. Arifudin, Mathematical model of seasonal influenza with treatment in constant population, IOP
Conf. Series: J. Phys. Conf. Series 824 (2017) 012034, DOI:10.1088/1742-6596/824/1/012034.
[11] N.K. Goswami and B. Shanmukha, A Mathematical Model of Influenza: Stability and Treatment, Proc. Int. Conf.
Math. Model. Simul. (ICMMS 16), (2017).
[12] Marsudi, Marjono, A. Andari, Sensitivity analysis of effect of screening and HIV therapy on the dynamics of
spread of HIV, Appl. Math. Sci. 8(155) (2014) 7749–7763.
[13] S. Athithan, M. Ghosh and X. Li,Mathematical modeling and optimal control of corruption dynamics, AsianEuropean J. Math. 11(6) (2018) 1850090-12. DOI: 10.1142/S1793557118500900.
[14] N. K. Goswami, A.K. Srivastav, M. Ghosh and B. Shanmukha, Mathematical modeling of zika virus disease with
nonlinear incidence and optimal control, IOP Conf. Series: Journal of Physics: Conf. Series 1000 (2018) 012114
[15] O. S. Sisodiya, O.P. Misra and J. Dhar, Pathogen induced infection and its control by vaccination: A mathematical
model for Cholera disease, Int. J. Appl. Comput. Math. 4 (2018) 74
[16] A. K. Srivastav, N. K. Goswami, M.Ghosh and X. Z. Li, Modeling and optimal control analysis of Zika virus with
media impact, Int. J. Dyn. Cont. (2017),
[17] J.M. Hefferman, R.J. Smith and L.M. Wahi, Perspective on the basic reproductive ratio, J. R. Soc. Interf. 2 (2005)
[18] K. Park, Preventive and social Medicine., M/S BanarsiDas Bhanot publishers, Jabalpur, India, 2002.
[19] K. Park, Essentials of Community Health Nursing, M/S BanarsiDas Bhanot publishers, Jabalpur, India, 2004.
[20] P. Rani, D. Jain and V.P. Saxena, Stability analysis of HIV/AIDS transmission with treatment and role of female
sex workers, IJNSNS, DE GRUYTER, (2017), DOI 10.1515/ijnsns-2015-0147.
[21] H. Purushwani and P. Sinha Mathematical modeling on successive awareness policies for Swine Flu, IJSTR 8(8)
(2019) 310–320.
[22] C. Purushwani and P. Sinha Impact of treatment on droplet infection: Age structured mathematical model, IJSTR
8(7) (2019) 643–657.
Volume 12, Issue 2
November 2021
Pages 2429-2451
  • Receive Date: 13 June 2019
  • Accept Date: 28 October 2020