A Simple Sirs Mathematical Model with Mass Action Type Incidence

Amit Kumar¹ , Pardeep Porwal² , V. H. Badshah³

1. School of Studies in Mathematics, Vikram University, Ujjain, India.
2. School of Studies in Mathematics, Vikram University, Ujjain, India.
3. School of Studies in Mathematics, Vikram University, Ujjain, India.

Correspondence should be addressed to: amit0830@gmail.com.

Section:Research Paper, Product Type: Isroset-Journal
Vol.4 , Issue.5 , pp.9-12, Oct-2017

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v4i5.912

Online published on Oct 30, 2017

Copyright © Amit Kumar, Pardeep Porwal, V. H. Badshah . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

959 Views    364 Downloads    202 Downloads

Abstract :
In this paper a simple SIRS mathematical model with mass action type incidence is formulated and studied. Steady state, equilibrium point and the basic reproduction number are obtained for the system of differential equation. Existence and stability of the diseases free and endemic stages are investigated. An example is also furnished which demonstrates validity of main result.

Key-Words / Index Term :
Mathematical Model, Equilibrium point, Stability, Incidence

References :
[1]. A. Kumar., P. Porwal, and V. H. Badshah., “Modified SIRS Epidemic Model with Immigration and Saturated Incidence rate”, MAYFEB Journal of Mathematics ISSN,2371-6193,(4) , 7-12, 2016.
[2]. H. W. Hethcote., “Qualitative Analysis for Communicable Disease Models”, Math., Bio science, 28, 335-356, 1976.
[3]. H. W. Hethcote., “Three Basic Epidemiological Models”, In Applied Mathematical Ecology, L. Gross, T.G. Hallam and S.A. Levin , Springer, Berlin, 119-144, 1989.
[4]. H. W. Hethcote., and P. Driessch Van Den., “Some Epidemiological models with Non-linear Incidence”. J. Math. Boil., 29, 271-287, 1991.
[5]. H. W. Hethchote., “The Mathematics of Infectious Disease”, SIAM Review 42, 599 -653, 2000.
[6]. J. M. Mena Lorca., and H. W. Hethcote., “Dynamic Models of Infectious Disease as Regulators of Population Sizes’, Journal Math. Bio. 30, 693 – 716, 1992.
[7]. P. Porwal., P. Ausif., and S. K. Tiwari., “An SIS Model for Human and Bacterial Population with Modified Saturated Incidence Rate and Logistic Growth”, International Journal of Modern Mathematical Science, 12(2), 98-111, 2011.
[8]. P. Porwal., and V. H. Badshah., “A Study of Avion Influenza (Birds- Flu) Epidemic with Vaccinated Human Population”, International Journal of Mathematical Modeling Simulation and Application 5(12),75.
[9]. P. Porwal., and V. H. Badshah., “Modified Epidemic Model with Saturated Incidence rate and Reduced Transmission Under Treatment”, International Journal of Mathematics Archieve, 4(12), 106-111, 2013.
[10]. P. Porwal., and V. H. Badshah., “Dynamical study of SIRS Epidemic Model with Vaccinated Susceptibilit”, Canadian Journal of Basic and Applied Science 2(4), 90-96, 2014.
[11]. P. Porwal., P. Shrivastava, and S. K. Tiwari., “Study of Single SIR Epidemic Model”, Plegia Library Advance in Applied Science Research, 6(4),1- 4,2014.
[12]. R. M. Anderson, and R.M. May., “ Population Biology of Infectious Disease”, Nature, Springer Verlag, Berlin , Heidelberg, New York, 180, 361-367, 1979.
[13]. R. K. Miller., and AN. Michal., “Ordinary Differential equations” New York, Academic Press (1982)
[14]. V. H. Badshah., and A. Kumar., “A Study of Mathematical Modeling in Mathematics”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.3, Issue.1, pp.1-3, 2016.
[15]. V. Capasso., and G. Serio., “A Generalization of the Kermack and Mc Kendrick Deterministic Epidemic Model”, Math Bio science. 42, 41 – 61, 1978.
[16]. W. O. Kermack., and A. G. Mc Kendrick., “Contribution to the Mathematical Theory of Epidemics”, Part1. Royal Society, London, 115, 700 – 721, 1927.