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

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

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

References:
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J. Vector Borne Dis., 47 (2010), 155-159. Google Scholar

[2]

Discrete Contin. Dyn. Syst., Ser. B, 11 (2009), 587-611. doi: 10.3934/dcdsb.2009.11.587.  Google Scholar

[3]

J. R. Soc. Interface, 7 (2010), 873-885. doi: 10.1098/rsif.2009.0386.  Google Scholar

[4]

Math Biosci., 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[5]

Nature, 446 (2007). doi: 10.1038/446733a.  Google Scholar

[6]

Proc. Natl. Acad. Sci. USA, 106 (2009), 6872-6877. doi: 10.1073/pnas.0810762106.  Google Scholar

[7]

J. Theor. Biol., 264 (2010), 501-509. doi: 10.1016/j.jtbi.2010.02.032.  Google Scholar

[8]

J. R. Soc. Interface, 7 (2010), 1247-256. doi: 10.1098/rsif.2010.0142.  Google Scholar

[9]

Health and Environment Linkages Initiative(HELI), [online document], Available from: \url{http://www.who.int/heli/risks/vectors/vector/en/index.html}., ().   Google Scholar

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[11]

Pub. Opin. Quart., 11 (1947), 412-423. Google Scholar

[12]

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[13]

Princeton University Press, New Jersey, 2008.  Google Scholar

[14]

Math Biosci., 255 (2010), 1-10. doi: 10.1016/j.mbs.2009.11.009.  Google Scholar

[15]

Math Comput. Model, 16 (1992), 103-111. doi: 10.1016/0895-7177(92)90155-E.  Google Scholar

[16]

Math Biosci. Engg., 5 (2008), 789-801. doi: 10.3934/mbe.2008.5.789.  Google Scholar

[17]

Comput. Math Methods Med., 8 (2007), 153-164. doi: 10.1080/17486700701425870.  Google Scholar

[18]

Int. J. Biomath., 1 (2008), 65-74. doi: 10.1142/S1793524508000023.  Google Scholar

[19]

PLoS. Negl. Trop. Dis., 4 (2010), e761. doi: 10.1371/journal.pntd.0000761.  Google Scholar

[20]

World Scientific, Singapore, 2009. doi: 10.1142/9789812797506.  Google Scholar

[21]

Oxford University Press, London, 1957. Google Scholar

[22]

Malaria comic book from Chillibreeze, [online document], Available from: \url{http://www.chillibreeze.com/ebooks/malaria.asp}., ().   Google Scholar

[23]

Math. Comput. Model., 53 (2011), 1221-1228. doi: 10.1016/j.mcm.2010.12.005.  Google Scholar

[24]

J. Biol. Sys., 19 (2011), 389-402. doi: 10.1142/S0218339011004020.  Google Scholar

[25]

Discrete Contin. Dyn. Syst., Ser. B, 4 (2004), 1173-1202. doi: 10.3934/dcdsb.2004.4.1173.  Google Scholar

[26]

Emerg. Infect Dis., 4 (1998), 398-403. doi: 10.3201/eid0403.980313.  Google Scholar

[27]

Murray, London, 1911. Google Scholar

[28]

Indian J. Med. Res., 103 (1996), 26-45. Google Scholar

[29]

J. Vect. Borne. Dis., 42 (2005), 30-35. Google Scholar

[30]

WHO chikungunya factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs327/en/index.html}., ().   Google Scholar

[31]

WHO Dengue factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs117/en/index.html}., ().   Google Scholar

[32]

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[33]

WHO Yellow fever factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs100/en/index.html}., ().   Google Scholar

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