Impact of Awareness on the Spread of Dengue Infection in Human Population

ABSTRACT

In this paper, a model is proposed to study the impact of awareness on the dynamics of dengue. It is assumed that due to awareness of the disease some susceptible take necessary precautionary measures to protect themselves from mosquito bite. A threshold is obtained for the stability of the disease-free equilibrium state. The awareness is found to affect the threshold. For the sufficiently large awareness rate, the endemic state does not exist and disease-free state remains globally stable. It is concluded that the increase in the awareness rate decreases the densities of infectious populations of human as well as mosquitoes.

Cite this paper

S. Gakkhar and N. Chavda, "Impact of Awareness on the Spread of Dengue Infection in Human Population,"*Applied Mathematics*, Vol. 4 No. 8, 2013, pp. 142-147. doi: 10.4236/am.2013.48A020.

S. Gakkhar and N. Chavda, "Impact of Awareness on the Spread of Dengue Infection in Human Population,"

References

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[1] “Dengue Guidelines of Diagnosis, Treatment, Prevention and Control,” WHO Report, 2009.

[2] D. J. Gubler, “Dengue,” In: T. P. Monath, Ed., The Arbovirus: Epidemiology and Ecology, Vol. 2, CRC, Boca Raton, 1986, p. 213.

[3] Z. Feng and V. Vealsco-Hernandez, “Competitive Exclu sion in a Vector-Host Model for the Dengue Fever,” Journal of Mathematical Biology, Vol. 35, No. 5, 1997, pp. 523-544. doi:10.1007/s002850050064

[4] L. Esteva and C. Vargas, “Analysis of a Dengue Disease Transmission Model,” Mathematical Biosciences, Vol. 150, No. 2, 1998, pp. 131-151. doi:10.1016/S0025-5564(98)10003-2

[5] L. Esteva and C. Vargas, “Influence of Vertical and Me chanical Transmission on the Dynamics of Dengue Dis ease,” Mathematical Biosciences, Vol. 167, No. 1, 2000, pp. 51-64. doi:10.1016/S0025-5564(00)00024-9

[6] F. A. B. Coutinho, M. N. Burattini, L. F. Lopez and E. Massad, “Threshold Conditions for a Nonautonomous Epi demic System Describing the Population Dynamics of Dengue,” Bulletin of Mathematical Biology, Vol. 68, No. 8, 2006, pp. 2263-2282. doi:10.1007/s11538-006-9108-6

[7] M. Derouich and A. Boutayeb, “Dengue Fever: Mathe matical Modelling and Computer Simulation,” Applied Mathematics and Computation, Vol. 177, No. 2, 2006, pp. 528-544. doi:10.1016/j.amc.2005.11.031

[8] N. M. Ferguson, C. A. Donnelly and R. M. Anderson, “Transmission Dynamics and Epidemiology of Dengue: Insights from Age-Stratified Sero-Prevalence Surveys,” Philosophical Transactions of the Royal Society of London B, Vol. 354, No. 1384, 1999, pp. 757-768. doi:10.1098/rstb.1999.0428

[9] C. J. Struchiner, P. M. Luz, C. T. Codeco, F. C. Coelho and E. Massad, “Current Research Issues in Mosquito Borne Diseases Modelling,” Contemporary Mathematics, Vol. 410, 2006, pp. 349-352. doi:10.1090/conm/410/07736

[10] J. J. Tewa, J. L. Dimi and S. Bowang, “Lyapunov Func tions for a Dengue Disease Transmission Model,” Chaos, Solitons and Fractals, Vol. 39, No. 2, 2009, pp. 936-941. doi:10.1016/j.chaos.2007.01.069

[11] H. M. Yang and C. P. Ferreira, “Assessing the Effects of Vector Control on Dengue Transmission,” Applied Ma thematics and Computation, Vol. 198, No. 1, 2008, pp. 401-413. doi:10.1016/j.amc.2007.08.046

[12] P. van den Driessche and J. Watmough, “Reproduction Numbers and Sub-Threshold Endemic Equilibria for Com partmental Models of Disease Transmission,” Mathema tical Biosciences, Vol. 180, No. 1-2, 2002, pp. 29-48. doi:10.1016/S0025-5564(02)00108-6

[13] M. Y. Li and J. S. Muldowney, “Global Stability for the SEIR Model in Epidemiology,” Mathematical Biosci ences, Vol. 125, No. 2, 1995, pp. 155-164. doi:10.1016/0025-5564(95)92756-5

[14] R. H. Martin Jr., “Logarithmic Norms and Projections Applied to Linear Differential Systems,” Journal of Ma thematical Analysis and Applications, Vol. 45, No. 2, 1974, pp. 432-454. doi:10.1016/0022-247X(74)90084-5

[15] B. Buonomo and D. Lacitignola, “On the Use of the Geo metric Approach to Global Stability for Three Dimen sional ODE Systems: A Bilinear Case,” Journal of Ma thematical Analysis and Applications, Vol. 348, No. 1, 2008, pp. 255-266. doi:10.1016/j.jmaa.2008.07.021