Abstract
In this article, we investigate the effect of an awareness campaign on the prevalence of infectious diseases, assuming the awareness campaign is organised periodically. On this basis, an SIS model is developed, considering susceptible and infected humans, using impulsive differential equations to describe the awareness campaign. To attain an effective control of the disease, the period and rate of awareness is determined using the mathematical model. Numerical simulations illustrate the analytical outcomes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
WHO: The world health report 2004: Changing history. http://www.who.int/whr/2004/en/ (2004)
Brodie, M., Hamel, E., Brady, L.A., et al.: AIDS at 21: Media coverage of the HIV epidemic 1981–2002. Columbia J. Rev. 42(6), A1
Cui, J., Sun, Y., Zhu, H.: The impact of media on the control of infectious diseases. J. Dyn. Differ. Equ. 20, 31–53 (2007)
Liu, Y., Cui, J.A., Zhu, H.: The impact of media coverage on the dynamics of infectious disease. Int. J. Biomath. 1(1), 65–74 (2008)
Smith, R.J., Cloutier, P., Harrison, J., Desforges, A.: A mathematical model for the eradication of Guinea Worm Disease. In: Mushayabasa, S., Bhunu, C.P. (eds) Understanding the dynamics of emerging and re-emerging infectious diseases using mathematical models, pp. 133–156. (2012)
Al Basir, F., Ray, S., Venturino, E.: Role of media coverage and delay in controlling infectious diseases: a mathematical model. Appl. Math. Comput. 337, 372–385 (2018)
Dupas, P.: Health behavior in developing countries. Annu. Rev. Econ. 3(1), 425–449 (2011)
Agaba, G.O., Kyrychko, Y.N., Blyuss, K.B.: Time-delayed SIS epidemic model with population awareness. Ecol. Complex. 31, 50–56 (2017)
Roy, P.K., Saha, S., Basir, A.F.: Effect of awareness programs in controlling the disease HIV/AIDS: an optimal control theoretic approach. Adv. Differ. Equ. 2015(1), 217 (2015)
Basir, F.A., Venturino, E., Roy, P.K.: Effects of awareness program for controlling mosaic disease in Jatropha curcas plantations. Math. Methods Appl. Sci. 40(7), 2441–2453 (2017)
Li, X., Bohner, M., Wang, C.K.: Impulsive differential equations: periodic solutions and applications. Automatica 52, 173–8 (2015)
Liu, X.N., Chen, L.S.: Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator. Chaos Solitons Fractals 16(2), 311–320 (2003)
Yu, H., Zhong, S., Agarwal, R.P.: Mathematics analysis and chaos in an ecological model with an impulsive control strategy. Commun. Nonlinear Sci. Numer. Simul. 16(2), 776–786 (2011)
Lakshmikantham, V., Bainov, D.D., Simeonovm, P.S.: Theory of impulsive differential equations, series in modern applied mathematics. World Scientific Publishing, pp. 6 (1989)
Acknowledgements
Author is grateful to the reviewers for their useful comments which enrich the content of the paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Al Basir, F. (2020). Dynamics of Infectious Diseases with Periodic Awareness Campaigns. In: Roy, P., Cao, X., Li, XZ., Das, P., Deo, S. (eds) Mathematical Analysis and Applications in Modeling. ICMAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 302. Springer, Singapore. https://doi.org/10.1007/978-981-15-0422-8_30
Download citation
DOI: https://doi.org/10.1007/978-981-15-0422-8_30
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-0421-1
Online ISBN: 978-981-15-0422-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)