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Modeling the impact of sanitation and awareness on the spread of infectious diseases

1 Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi - 221005, India
2 College of Science and Engineering, Department of Physics and Mathematics, Aoyama Gakuin University, Kanagawa 252-5258, Japan

Sanitation and awareness programs play a fundamental role and are much effective public health interventions to control the spread of infectious diseases. In this paper, a nonlinear mathematical model for the control of infectious diseases, such as typhoid fever is proposed and analyzed by considering budget required for sanitation and awareness programs as a dynamic variable. It is assumed that the budget allocation regarding the protection against the disease to warn people and for sanitation increases logistically and its per-capita growth rate increases with the increase in number of infected individuals. In the model formulation, it is assumed that the susceptible individuals contract infection through the direct contact with infected individuals as well as indirectly through bacteria shed in the environment. It is further assumed that a fraction of budget is used to warn people via propagating awareness whereas the remaining part is used for sanitation to reduce the density of bacteria. The condition when budget should spend on sanitation/awareness to reduce the number of infected individuals is obtained. Model analysis reveals that the sanitation and awareness programs have capability to reduce the epidemic threshold and thus control the spread of infection. However, delay in providing funds destabilizes the system and may cause stability switches through Hopf-bifurcation. Numerical simulations are also carried out to support analytical findings.
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Keywords budget allocation; delay; sanitation; awareness; hopf-bifurcation; stability switch

Citation: Rajanish Kumar Rai, Arvind Kumar Misra, Yasuhiro Takeuchi. Modeling the impact of sanitation and awareness on the spread of infectious diseases. Mathematical Biosciences and Engineering, 2019, 16(2): 667-700. doi: 10.3934/mbe.2019032


  • 1. G.O. Agaba, Y.N. Kyrychko and K.B. Blyuss, Time-delayed SIS epidemic model with population awareness, Ecol. Complex., 31 (2017), 50–56.
  • 2. J. Cui, Y. Sun and H. Zhu, The impact of media on the control of infectious diseases, J. Dyn. Differ. Equ., 20 (2008), 31–53.
  • 3. J. Cui, X. Tao and H. Zhu, An SIS infection model incorporating media coverage, Rocky Mountain J. Math., 38 (2008), 13–23.
  • 4. S. Collinson, K. Khan and J.M. Heffernan, The effects of media reports on disease spread and important public health measurements, PLoS One, 10 e0141423 (2015), 1–21.
  • 5. P.V. Driessche and J.Watmough, Reproduction numbers and sub-thershold endemic equalibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
  • 6. B. Dubey, P Dubey and U.S. Dubey, Role of media and treatment on an SIR model, Nonlinear Anal. Model. Control, 21 (2016), 185–200.
  • 7. H.I. Freedman and J.W.H. So, Global stability and persistence of simple food chains, Math. Biosci., 76 (1985), 69–86.
  • 8. H.I. Freedman and V.S.H. Rao, The trade-off between mutual interference and time lags in predator-prey systems, Bull. Math. Biol., 45 (1983), 991–1004.
  • 9. J. Gonzalez-Guzman, An epidemiological model for direct and indirect transmission of Typhoid fever, Math. Boisci., 96 (1989), 33–46.
  • 10. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, Dordrecht, Norwell, MA (1992).
  • 11. D. Greenhalgh, S. Rana, S. Samanta, T. Sardar, S. Bhattacharya and J. Chattopadhyay, Awareness programs control infectious disease-multiple delay induced mathematical model, Appl. Math. Comput., 251 (2015), 539–563.
  • 12. H.F. Huo, P. Yang and H. Xiang, Stability and bifurcation for an SEIS epidemic model with the impact of media, Physica A, 490 (2018), 702–720.
  • 13. Importance of Gandhian thoughts about Cleanliness, Available from: https://www.mkgandhi.org/articles/gandhian-thoughts-about-cleanliness. html.
  • 14. Y. Kuang, Delay differtial equations with application in population dynamics, Mathematics in Science and Engineering, 191 (1992).
  • 15. S.M. Kerstens, M. Spiller, I. Leusbrock and G. Zeeman, A new approach to nationwide sanitation planning for developing countries: Case study of Indonesia, Sci. Total. Environ., 550 (2016), 676– 689.
  • 16. A. Kumar, P.K. Srivastava and Y. Takeuchi, Modeling the role of information and limited optimal treatment on disease prevalence, J. Theor. Biol., 414 (2017), 103–119.
  • 17. V. Lakshmikantham and S. Leela, Differential and integral ineualities; theory and applications. Acedemic press New Yark and Landan (1969).
  • 18. R. Liu, J. Wu and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput. Math. Methods Med., 8 (2007), 153–164.
  • 19. Y. Liu and J. Cui, The impact of media convergence on the dynamics of infectious diseases, Int. J. Biomath, 1 (2008), 65–74.
  • 20. Y. Li and J. Cui, The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009), 2353–2365.
  • 21. X. Lu, S. Wang, S. Liu and J. Li, An SEI infection model incorporating media impact, Math. Biosci. Eng., 14 (2017), 1317–1335.
  • 22. D. Mara, J. Lane, B. Scott and D. Trouba, Sanitation and Health, PLoS Med, 7 (2010), e1000363.
  • 23. A.K. Misra, A. Sharma and J.B. Shukla, Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases, Math. Comput. Model., 53 (2011a), 1221–1228.
  • 24. A.K. Misra, A. Sharma and V. Singh, Effect of awareness programs in cotroling the prevelence of an epidemic with time delay, J. Biol. Syst., 19(2) (2011b), 389–402.
  • 25. S. Mushayabasa, C.P. Bhunu and E.T. Ngarakana-Gwasira, Assessing the impact of drug resistance on the transmission dynamics of Typhoid fever, Comput. Biol. J., 303645 (2013), 1–13.
  • 26. A.K. Misra, A. Sharma and J.B. Shukla, Stability analysis and optimal control of an epidemic model with awareness program by media, Bio Systems, 138 (2015), 53–62.
  • 27. A.K. Misra, R.K. Rai and Y. Takeuchi, Modeling the effect of time delay in budget allocation to control an epidemic through awareness, Int. J. Biomath., 11 (2018), 1–20.
  • 28. A.K. Misra and R.K. Rai, A mathematical model for the control of infectious diseases: Effects of TV and radio advertisements, Int. J. Bifurc. Chaos, 28(2018), 1–27.
  • 29. A.K. Misra, R.K. Rai and Y. Takeuchi, Modeling the control of infectious diseases: Effects of TV and social media advertisements, Math. Biosci. Eng., 15 (2018), 1315–1343.
  • 30. F. Nyabadza, C. Chiyaka, Z. Mukandavire and S.D.H. Musekwa, Analysis of an HIV/AIDS model with public-health information campaigns and individual withdrawal, J. Biol. Syst., 18 (2010), 357–375.
  • 31. K.A. Pawelek, A.O. Hirsch and L. Rong, Modeling the impact of twitter on influenza epidemics, Math. Biosci. Eng., 11 (2014), 1337–1356.
  • 32. P.K. Roy, S. Saha and F. Al Basir, Effect of awareness programs in controlling the disease HIV/AIDS: an optimal control theoretic approach, Adv. Differ. Equ., 217 (2015), 1–18.
  • 33. Swachh Bharat Urban, Ministry of Housing and Urban Affairs, Government of India, Available from: http://www.swachhbharaturban.in/sbm/home/#/SBM.
  • 34. C. Sun, W. Yang, J. Arino and K. Khan, Effect of media-induced social distancing on disease transmission in a two patch setting, Math. Biosci., 230 (2011), 87–95.
  • 35. S. Samanta, S. Rana, A. Sharma, A.K. Misra and J. Chattopadhyay, Effect of awareness programs by media on the epidemic outbreaks: A mathematical model, Appl. Math. Comput., 219 (2013), 6965–6977.
  • 36. P. Song and Y. Xiao, Global Hopf-bifurcation of a delayed equation describing the lag effect of media impact on the spread of infectious disease, J. Math. Biol., 76 (2018), 1249–1267.
  • 37. J.M. Tchuenche, N. Dube, C.P. Bhunu, R.J. Smith and C.T. Bauch, The impact of media coverage on the transmission dynamics of human influenza, BMC Public Health, 11 (2011), 1–16.
  • 38. J.M. Tchuenche and C.T. Bauch, Dynamics of an infectious disease where media coverage influences transmission, ISRN Biomath, 581274 (2012), 1–11.
  • 39. World Health Organization and UNICEF, Progress on Drinking Water and Sanitation: 2014 Update, United States: WHO/UNICEF Joint Monitoring Programme, (2014), Available from: http: //www.who.int/water_sanitation_health/publications/2014/jmp-report/en/.
  • 40. WHO, World Health Organisation Media Centre, Sanitation Fact Sheet (2017), Available from: http://www.who.int/mediacentre/factsheets/fs392/en/.
  • 41. WHO, World Health Organisation, Media Centre, Typhoid Fact Sheet,(2018), Available from: http://www.who.int/mediacentre/factsheets/typhoid/en/.
  • 42. C. Yang, X.Wang, D. Gao and J.Wang, Impact of awareness programs on Cholera dynamics: Two modeling approaches, Bull. Math. Biol., 79 (2017), 2109–2131.


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