Impact of profession and surroundings on spread of swine flu: A mathematical study

Hema Purushwani; Poonam Sinha

doi:10.26637/MJM0702/0020

Abstract

Swine flu is a respiratory disease caused by $\mathrm{H} 1 \mathrm{~N} 1$ virus which was introduced in 2009 . People who work in poultry farms and are in contact with live swine have high risk of swine flu infection. Use of mask by workers can be taken as prevention against disease. Here, we have formulated a SEIR mathematical model in two compartments to see the effect of profession and surroundings on spread of swine flu. Moreover, disease free equilibrium point, endemic equilibrium point and basic reproduction number have been calculated. It is seen that disease free equilibrium point always exists and is stable when $R_0<1$. Similarly, endemic equilibrium point exist and is stable when $R_0>1$. Sensitivity analysis of equilibrium point and basic reproduction number indicates the impact of parameter on spread of disease. Optimal value for efficiency of mask $(a)$ is derived. Further, using MATLAB, numerical simulation has been done with respect to suitable parameter values and appropriate graphs have been obtained for all populations to understand the transmission behavior of swine flu.

Keywords:

Swine flu infection and its prevention strategy, SEIR Mathematical model, Basic reproduction number, Stability analysis, Optimal control, Sensitivity analysis

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Hema Purushwani Department of Mathematics, S. M. S. Govt Model Science College,Gwalior- 474010, MP, India.
Poonam Sinha Department of Mathematics, S. M. S. Govt Model Science College,Gwalior- 474010, MP, India.

Pages: 276-286
Date Published: 01-04-2019
Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)

M. Imran, T. Malik, A. R. Ansari, A. Khan, Mathematical analysis of swine influenza epidemic model with optimal control,. Japan Journal of Industrial and Applied Mathematics, 33(1)(2016), 269-296.

G. C. Gray, T. McCarthy, A. W. Capuano, S. F. Setterquist, C. W. Olsen, M. C. Alavanja, C. F. Lynch, Swine Workers and Swine Influenza Virus Infections, Emerging Infectious Diseases, 13(12)(2007), 1871-1878.

P. Das, N. H. Gazi, K. Das, D. Mukherjee, Stability Analysis of Swine Flu Transmission- A Mathematical Approach, Computational and Mathematical Biology, $3(1)(2014)$.

A. K. Srivastav, M. Ghosh, Modeling and analysis of the symptomatic and asymptomatic infections of swine flu with optimal control, Modeling Earth Systems and Environment, 4(2016), 1-9.

Z. Jin, J. Zhang, L. P. Song, G. Q. Sun, J. Kan, H. Zhu, Modelling and analysis of influenza A (H1N1) on networks, Jin et al. BMC Public Health, 11(1)(2011).

D. Aldila, N. Nuraini, E. Soewono, Optimal Control Problem in Preventing of Swine Flu Disease Transmission, Applied Mathematical Sciences, 8(71)(2014), 3501 - 3512 .

C. Cador, M. Andraud, L. Willem, N. Rose, Control of endemic swine flu persistence in farrow-to-finish pig farms: a stochastic metapopulation modeling assessment, Veterinary Research, 48(1)(2017).

J. M. Heffernan, R. J. Smith,L. M. Wahl, Perspectives on the basic reproductive ratio, Journal of The Royal Society Interface, 2(4)(2005), 281-293.

K. Park, Preventive and Social Medicine, M/S Banarsi Das Bhanot Publishers, Jabalpur, India, (2005).

WHO, Influenza fact sheet, http://www.who.int/mediacentre/factsheets/fs211/en/, (2008).

O. P. Misra, D. K. Mishra, Spread and control of influenza in two groups: A model, Applied Mathematics and Computation, $219(15)(2013), 7982-7996$.

N. Chitnis, J. M. Hyman, J. M. Cushing, Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model, Bulletin of Mathematical Biology, 70(5)(2008), $1272-1296$.

A. Marsudi, 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.

S. Athithan, M. Ghosh, X. Z. Li, Mathematical modeling and optimal control of corruption dynamics, AsianEuropean Journal of Mathematics, (2017).

N. K. Goswami, A. K. Srivastav, M. Ghosh, B. Shanmukha, Mathematical modeling of zika virus disease with nonlinear incidence and optimal control, Journal of Physics: Conference Series, (2018).

O. S. Sisodiya, O. P. Misra, J. Dhar, Pathogen Induced Infection and Its Control by Vaccination: A Mathematical Model for Cholera Disease, International Journal of Applied and Computational Mathematics, 4(2)(2018).

A. K. Srivastav, N. K. Goswami, M. Ghosh, X. Z. Li, Modeling and optimal control analysis of Zika virus with media impact, International Journal of Dynamics and Control, (2018).

P. Rani, D. Jain, V. P. Saxena, Stability Analysis of HIV/AIDS Transmission with Treatment and Role of Female Sex Workers, International Journal of Nonlinear Sciences and Numerical Simulation, 18(6)(2017).