A mathematical model for control of vector borne diseases through media campaigns

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September 2013, 18(7): 1909-1927. doi: 10.3934/dcdsb.2013.18.1909

A mathematical model for control of vector borne diseases through media campaigns

A. K. Misra ^1, , Anupama Sharma ^1, and Jia Li ^2,

1.	Department of Mathematics, Faculty of Science, Banaras Hindu University, Varanasi-221 005, India, India
2.	Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899

Received June 2012 Revised October 2012 Published May 2013

Abstract
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Vector borne diseases spread rapidly in the population. Hence their control intervention must work quickly and target large area as well. A rational approach to combat these diseases is mobilizing people and making them aware through media campaigns. In the present paper, a non-linear mathematical model is proposed to assess the impact of creating awareness by the media on the spread of vector borne diseases. It is assumed that as a response to awareness, people will not only try to protect themselves but also take some potential steps to inhibit growth of vectors in the environment. The model is analyzed using stability theory of differential equations and numerical simulation. The equilibria and invasion threshold for infection i.e., basic reproduction number, has been obtained. It is found that the presence of awareness in the population makes the disease invasion difficult. Also, continuous efforts by the media along with the swift dissemination of awareness can completely eradicate the disease from the system.

Keywords: stability., media campaigns, vector borne diseases, awareness, Epidemic model.

Mathematics Subject Classification: Primary: 92D30, 92B0.

Citation: A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909

References:

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[15]	J. Li, Effects of behavior change on the spread of AIDS epidemic, Math Comput. Model, 16 (1992), 103-111. doi: 10.1016/0895-7177(92)90155-E.
[16]	J. Li, A malaria model with partial immunity in humans, Math Biosci. Engg., 5 (2008), 789-801. doi: 10.3934/mbe.2008.5.789.
[17]	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. doi: 10.1080/17486700701425870.
[18]	Y. Liu and J. Cui, The impact of media coverage on the dynamics of infectious disease, Int. J. Biomath., 1 (2008), 65-74. doi: 10.1142/S1793524508000023.
[19]	P. M. Luz, C. J. Struchiner and A. P. Galvani, Modeling transmission dynamics and control of vector- borne neglected tropical diseases, PLoS. Negl. Trop. Dis., 4 (2010), e761. doi: 10.1371/journal.pntd.0000761.
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[22]	Malaria comic book from Chillibreeze, [online document], Available from: \url{http://www.chillibreeze.com/ebooks/malaria.asp}., ().
[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 (2011), 1221-1228. doi: 10.1016/j.mcm.2010.12.005.
[24]	A. K. Misra, A. Sharma and V. Singh, Effect of awareness programs in controlling the prevalence of an epidemic with time delay, J. Biol. Sys., 19 (2011), 389-402. doi: 10.1142/S0218339011004020.
[25]	G. A. Ngwa, Modelling the dynamics of endemic malaria in growing populations, Discrete Contin. Dyn. Syst., Ser. B, 4 (2004), 1173-1202. doi: 10.3934/dcdsb.2004.4.1173.
[26]	T. C. Nchinda, Malaria: A reemerging disease in Africa, Emerg. Infect Dis., 4 (1998), 398-403. doi: 10.3201/eid0403.980313.
[27]	R. Ross, "The Prevention of Malaria," 2^nd edition, Murray, London, 1911.
[28]	V. P. Sharma, Re-emergence of malaria in India, Indian J. Med. Res., 103 (1996), 26-45.
[29]	P. Tyagi, A. Roy and M. S. Malhotra, Knowledge, awareness and practices towards malaria in communities of rural, semi-rural and bordering areas of east Delhi (India), J. Vect. Borne. Dis., 42 (2005), 30-35.
[30]	WHO chikungunya factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs327/en/index.html}., ().
[31]	WHO Dengue factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs117/en/index.html}., ().
[32]	WHO Malaria factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs094/en/index.html}., ().
[33]	WHO Yellow fever factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs100/en/index.html}., ().

show all references

References:

[1]	A. A. Adedotun, O. A. Morenikeji and A. B. Odaibo, Knowledge, attitudes and practices about malaria in an urban community in south-western Nigeria, J. Vector Borne Dis., 47 (2010), 155-159.
[2]	K. Blayneh, Y. Cao and H-D. Kwon, Optimal control of vector-borne diseases: Treatment and prevention, Discrete Contin. Dyn. Syst., Ser. B, 11 (2009), 587-611. doi: 10.3934/dcdsb.2009.11.587.
[3]	O. Diekmann, J. A. P. Heesterbeek and M. G. Roberts, The construction of next-generation matrices for compartmental epidemic models, J. R. Soc. Interface, 7 (2010), 873-885. doi: 10.1098/rsif.2009.0386.
[4]	P. van den Driessche and J. Watmough, Reproduction numbers and sub-thershold endemic equalibria for compartmental models of disease transmission, Math Biosci., 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6.
[5]	N. Ferguson, Capturing human behaviour, Nature, 446 (2007). doi: 10.1038/446733a.
[6]	S. Funk, E. Gilad, C. Watkins and V. A. A. Jansen, The spread of awareness and its impact on epidemic outbreaks, Proc. Natl. Acad. Sci. USA, 106 (2009), 6872-6877. doi: 10.1073/pnas.0810762106.
[7]	S. Funk, E. Gilad and V. A. A. Jansen, Endemic disease, awareness, and local behavioural response, J. Theor. Biol., 264 (2010), 501-509. doi: 10.1016/j.jtbi.2010.02.032.
[8]	S. Funk, M. Salathé and V. A. A. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: A review, J. R. Soc. Interface, 7 (2010), 1247-256. doi: 10.1098/rsif.2010.0142.
[9]	Health and Environment Linkages Initiative(HELI), [online document], Available from: \url{http://www.who.int/heli/risks/vectors/vector/en/index.html}., ().
[10]	G. R. Hosack, P. A. Rossignol and P. van den Driessche, The control of vector-borne disease epidemics, J. Theor. Biol., 255 (2008), 16-25. doi: 10.1016/j.jtbi.2008.07.033.
[11]	H. H. Hyman and P. B. Sheatsley, Some reasons why information campaigns fail, Pub. Opin. Quart., 11 (1947), 412-423.
[12]	H. Joshi, S. Lenhart, K. Albright and K. Gipson, Modeling the effect of information campaigns on the HIV epidemic in Uganda, Math Biosci. and Engg., 5 (2008), 757-770. doi: 10.3934/mbe.2008.5.757.
[13]	M. J. Keeling and P. Rohani, "Modeling Infectious Diseases in Humans and Animals," Princeton University Press, New Jersey, 2008.
[14]	I. Z. Kiss, J. Cassell, M. Recker and P. L. Simon, The impact of information transmission on epidemic outbreaks, Math Biosci., 255 (2010), 1-10. doi: 10.1016/j.mbs.2009.11.009.
[15]	J. Li, Effects of behavior change on the spread of AIDS epidemic, Math Comput. Model, 16 (1992), 103-111. doi: 10.1016/0895-7177(92)90155-E.
[16]	J. Li, A malaria model with partial immunity in humans, Math Biosci. Engg., 5 (2008), 789-801. doi: 10.3934/mbe.2008.5.789.
[17]	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. doi: 10.1080/17486700701425870.
[18]	Y. Liu and J. Cui, The impact of media coverage on the dynamics of infectious disease, Int. J. Biomath., 1 (2008), 65-74. doi: 10.1142/S1793524508000023.
[19]	P. M. Luz, C. J. Struchiner and A. P. Galvani, Modeling transmission dynamics and control of vector- borne neglected tropical diseases, PLoS. Negl. Trop. Dis., 4 (2010), e761. doi: 10.1371/journal.pntd.0000761.
[20]	Z. Ma and Jia Li, "Dynamical Modeling and Analysis of Epidemics," World Scientific, Singapore, 2009. doi: 10.1142/9789812797506.
[21]	G. Macdonald, "The Epidemiology and Control of Malaria," Oxford University Press, London, 1957.
[22]	Malaria comic book from Chillibreeze, [online document], Available from: \url{http://www.chillibreeze.com/ebooks/malaria.asp}., ().
[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 (2011), 1221-1228. doi: 10.1016/j.mcm.2010.12.005.
[24]	A. K. Misra, A. Sharma and V. Singh, Effect of awareness programs in controlling the prevalence of an epidemic with time delay, J. Biol. Sys., 19 (2011), 389-402. doi: 10.1142/S0218339011004020.
[25]	G. A. Ngwa, Modelling the dynamics of endemic malaria in growing populations, Discrete Contin. Dyn. Syst., Ser. B, 4 (2004), 1173-1202. doi: 10.3934/dcdsb.2004.4.1173.
[26]	T. C. Nchinda, Malaria: A reemerging disease in Africa, Emerg. Infect Dis., 4 (1998), 398-403. doi: 10.3201/eid0403.980313.
[27]	R. Ross, "The Prevention of Malaria," 2^nd edition, Murray, London, 1911.
[28]	V. P. Sharma, Re-emergence of malaria in India, Indian J. Med. Res., 103 (1996), 26-45.
[29]	P. Tyagi, A. Roy and M. S. Malhotra, Knowledge, awareness and practices towards malaria in communities of rural, semi-rural and bordering areas of east Delhi (India), J. Vect. Borne. Dis., 42 (2005), 30-35.
[30]	WHO chikungunya factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs327/en/index.html}., ().
[31]	WHO Dengue factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs117/en/index.html}., ().
[32]	WHO Malaria factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs094/en/index.html}., ().
[33]	WHO Yellow fever factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs100/en/index.html}., ().

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