Dynamics of a disease model for three infection phases with media awareness as a control strategy

Volume 31, Issue 1, pp 56--69 http://dx.doi.org/10.22436/jmcs.031.01.05

Publication Date: April 14, 2023 Submission Date: February 15, 2022 Revision Date: December 09, 2022 Accteptance Date: December 15, 2022

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Authors

S. Agrawal - Amity School Of Applied Sciences, Amity University, Lucknow, Uttar Pradesh 226028, India. N. Mishra - Amity School Of Applied Sciences, Amity University, Lucknow, Uttar Pradesh 226028, India. J. Dhar - ABV Indian Institute of Information Technology and Management, Gwalior, Madhya Pradesh 474010, India.

Abstract

In this paper, a non-linear mathematical model with three irresistible classes for the impacts of media awareness programs on the spread of irresistible infections, for example, influenza, has been proposed and analyzed. In the modeling process, it is expected that illness spreads because of the contact between the susceptibles and infectives, as it were. The growth rate of media awareness programs influencing the populace corresponds to the number of infective people. We examine the dynamical behavior and systematic investigation of the framework for the model, which demonstrates that the model has two equilibrium points, i.e., disease-free equilibrium (DFE) and interior (endemic) equilibrium. The outcomes show that the primary reproduction number determines the dynamics of the model. For the basic reproduction number \({{\cal R}}_{0} < 1\), the disease-free equilibrium is locally as well as globally asymptotically stable under a specific parameter set. If \({{\cal R}}_{0} > 1\), the model at the interior equilibrium is locally asymptotically stable. At long last, numerical arrangements of the model validate the analytical outcomes and facilitate a sensitivity analysis of the model parameters.

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Keywords

• Epidemic model
• three phases of treatment
• non-pharmaceutical interventions
• fundamental reproduction number
• global stability
• local stability
• sensitivity analysis

MSC

•  92D30
•  34D23
•  93D20

References

• [1] F. Bachmann, G. Koch, M. Pfister, G. Szinnai, J. Schropp, OptiDose: Computing the individualized optimal drug dosing regimen using optimal control, J. Optim. Theory Appl., 189 (2021), 46–65
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] G. Birkhoff, G.-C. Rota, Ordinary differential equations, Wiley, New York (1989)
  • View Article
  • Google Scholar


• [3] R. J. Blendon, J. M. Benson, C. M. DesRoches, E. Raleigh, K. Taylor-Clark, The publics response to severe acute respiratory syndrome in toronto and the united states, Clin. Infect. Dis., 38 (2004), 925–931
  • View Article
  • Google Scholar


• [4] C. Castillo-Chavez, Z. Feng, W. Huang, On the computation of R0 and its role on global stability, in: Mathematical approaches for emerging and reemerging infectious diseases: An introduction, Springer-Verlag, 125 (2002), 229–250
  • View Article
  • Google Scholar


• [5] C. Castillo-Chavez, B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361–404
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] M. Corless, G. Leitmann, Analysis and control of a communicable disease, Nonlinear Anal., 40 (2000), 145–172
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] J. Cui, Y. Sun, H. Zhu, The impact of media on the control of infectious diseases, J. Dyn. Differ. Equ., 20 (2008), 31–53
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] J.-A. Cui, X. Tao, H. Zhu, An SIS infection model incorporating media coverage, Rocky Mountain J. Math., 38 (2008), 1323–1334
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] S. Del Valle, H. Hethcote, J. M. Hyman, C. Castillo-Chavez, Effects of behavioral changes in a smallpox attack model, Math. Biosci., 195 (2005), 228–251
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] J. Dhar, A. K. Sharma, The role of the incubation period in a disease model, Appl. Math. E-Notes, 9 (2009), 146–153
  • View Article
  • Google Scholar
  • MATH


• [11] J. Dhar, A. K. Sharma, The role of viral infection in phytoplankton dynamics with the inclusion of incubation class, Nonlinear Anal. Hybrid Syst., 4 (2010), 9–15
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] P. V. D. Driessche, J. Watmough, Mathematical epidemiology, Springer, Berlin (2008)
  • View Article


• [13] S. Funk, E. Gilad, C. Watkins, V. A. A. Jansen, The spread of awareness and its impact on epidemic outbreaks, Proc. Natl. Acad. Sci., 106 (2009), 6872–6877
  • View Article
  • Google Scholar
  • MATH


• [14] M. Ghosh, P. Chandra, P. Sinha, J. B. Shukla, Modelling the spread of bacterial disease: effect of service providers from an environmentally degraded region, Appl. Math. Comput., 160 (2005), 615–647
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] M. Ghosh, P. Chandra, P. Sinha, J. B. Shukla, Modelling the spread of bacterial infectious disease with environmental effect in a logistically growing human population, Nonlinear Anal. Real World Appl., 7 (2006), 341–363
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] M. A. Khan, S. F. Saddiq, S. A. Khan, S. Islam, F. Ahmad, Application of homotopy perturbation method to an SIR epidemic model, J. Appl. Environ. Biol. Sci., 4 (2014), 49–54
  • View Article
  • Google Scholar


• [17] N. Khazeni, D. Hutton, A. Garber, N. Hupert, D. Owens, Effectiveness and cost-effectiveness of vaccination against pandemic (H1N1) 2009, Ann. Intern. Med., 151 (2009), 829–839
  • View Article
  • Google Scholar


• [18] I. Z. Kiss, J. Cassell, M. Recker, P. L. Simon, The impact of information transmission on epidemic outbreaks, Math. Biosci., 255 (2010), 1–10
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] J. Li, Effects of behavior change on the spread of AIDS epidemic, Math. Comput. Model., 16 (1992), 103–111
  • View Article
  • Google Scholar
  • MATH


• [20] Y. Liu, J.-A. Cui, The impact of media convergence on the dynamics of infectious diseases, Int. J. Biomath., 1 (2008), 65–74
  • View Article


• [21] R. Liu, J. Wu, H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases, Comput. Math. Methods Med., 8 (2007), 153–164
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [22] A. K. Misra, A. Sharma, J. B. Shukla, Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases, Math. Comput. Model., 53 (2011), 1221–1228
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [23] S. Mushayabasa, C. P. Bhunu, R. J. Smith, Assessing the impact of educational campaigns on controlling HCV among women in prison settings, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1714–1724
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [24] R. Naresh, S. Pandey, A. K. Mishra, Analysis of a vaccination model for carrier dependent infectious diseases with environmental effects, Nonlinear Anal. Model. Control, 13 (2008), 331–350
  • View Article
  • Google Scholar
  • MATH


• [25] R. Naresh, A. Tripathi, D. Sharma, Modelling and analysis of the spread of AIDS epidemic with immigration of HIV infectives, Math. Comp. Model., 49 (2009), 880–892
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [26] J. Pang, J.-A. Cui, An SIRS epidemiological model with nonlinear incidence rate incorporating media coverage, in: Second International Conference on Information and Computing Science, IEEE, 3 (2009), 116–119
  • View Article
  • Google Scholar


• [27] M. A. Safi, A. B. Gumel, Mathematical analysis of a disease transmission model with quarantine, isolation and an imperfect vaccine, Comput. Math. Appl., 61 (2011), 3044–3070
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [28] G. P. Sahu, J. Dhar, Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate, Appl. Math. Model., 36 (2012), 908–923
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [29] G. P. Sahu, J. Dhar, Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity, J. Math. Anal. Appl., 421 (2015), 1651–1672
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [30] S. Singh, P. Chandra, J. B. Shukla, Modeling and analysis of the spread of carrier dependent infectious diseases with environmental effects, J. Biol. Syst., 11 (2003), 325–335
  • View Article
  • Google Scholar
  • MATH


• [31] P. K. Srivastava, M. Banerjee, P. Chandra, Dynamical model of in-host HIV infection: with drug therapy and multi viral strains, J. Biol. Syst., 20 (2012), 303–325
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [32] C. Sun, W. Yang, J. Arino, K. Khan, Effect of media-induced social distancing on disease transmission in a two patch setting, Math. Biosci., 230 (2011), 87–95
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [33] J. M. Tchuenche, N. Dube, C. P. Bhunu, R. J. Smith, C. T. Bauch, The impact of media coverage on the transmission dynamics of human influenza, BMC Public Health, 11 (2011), 1–14
  • View Article
  • Google Scholar


• [34] S. M. Tracht, S. Y. Del Valle, J. M. Hyman, Mathematical modeling of the effectiveness of facemasks in reducing the spread of novel influenza A (H1N1), PLoS ONE, 5 (2010), 1–12
  • View Article
  • Google Scholar


• [35] X. Wang, X. Song, S. Tang, L. Rong, Dynamics of an HIV model with multiple infection stages and treatment with different drug classes, Bull. Math. Biol., 78 (2016), 322–349
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH