American Institute of Mathematical Sciences

Advanced
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

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 & Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909
References:
[1]

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

[10]

J. Theor. Biol., 255 (2008), 16-25. doi: 10.1016/j.jtbi.2008.07.033.  Google Scholar

[11]

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

[12]

Math Biosci. and Engg., 5 (2008), 757-770. doi: 10.3934/mbe.2008.5.757.  Google Scholar

[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]

WHO Malaria factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs094/en/index.html}., ().   Google Scholar

[33]

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

show all references

References:
[1]

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

[10]

J. Theor. Biol., 255 (2008), 16-25. doi: 10.1016/j.jtbi.2008.07.033.  Google Scholar

[11]

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

[12]

Math Biosci. and Engg., 5 (2008), 757-770. doi: 10.3934/mbe.2008.5.757.  Google Scholar

[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]

WHO Malaria factsheet, [online document], Available from: \url{http://www.who.int/mediacentre/factsheets/fs094/en/index.html}., ().   Google Scholar

[33]

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

[1]

Chunhua Shan. Slow-fast dynamics and nonlinear oscillations in transmission of mosquito-borne diseases. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021097
[2]

Shangzhi Li, Shangjiang Guo. Permanence and extinction of a stochastic SIS epidemic model with three independent Brownian motions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2693-2719. doi: 10.3934/dcdsb.2020201
[3]

Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2997-3022. doi: 10.3934/dcdsb.2020217
[4]

Izumi Takagi, Conghui Zhang. Existence and stability of patterns in a reaction-diffusion-ODE system with hysteresis in non-uniform media. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3109-3140. doi: 10.3934/dcds.2020400
[5]

Michael Grinfeld, Amy Novick-Cohen. Some remarks on stability for a phase field model with memory. Discrete & Continuous Dynamical Systems, 2006, 15 (4) : 1089-1117. doi: 10.3934/dcds.2006.15.1089
[6]

Jing Feng, Bin-Guo Wang. An almost periodic Dengue transmission model with age structure and time-delayed input of vector in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3069-3096. doi: 10.3934/dcdsb.2020220
[7]

Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367
[8]

Azeddine Elmajidi, Elhoussine Elmazoudi, Jamila Elalami, Noureddine Elalami. Dependent delay stability characterization for a polynomial T-S Carbon Dioxide model. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021035
[9]

Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences & Engineering, 2010, 7 (2) : 313-345. doi: 10.3934/mbe.2010.7.313
[10]

Julian Tugaut. Captivity of the solution to the granular media equation. Kinetic & Related Models, 2021, 14 (2) : 199-209. doi: 10.3934/krm.2021002
[11]

Davi Obata. Symmetries of vector fields: The diffeomorphism centralizer. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021063
[12]

Lara Abi Rizk, Jean-Baptiste Burie, Arnaud Ducrot. Asymptotic speed of spread for a nonlocal evolutionary-epidemic system. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021064
[13]

Guillaume Bal, Wenjia Jing. Homogenization and corrector theory for linear transport in random media. Discrete & Continuous Dynamical Systems, 2010, 28 (4) : 1311-1343. doi: 10.3934/dcds.2010.28.1311
[14]

Fatemeh Abtahi, Zeinab Kamali, Maryam Toutounchi. The BSE concepts for vector-valued Lipschitz algebras. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1171-1186. doi: 10.3934/cpaa.2021011
[15]

Ahmad Mousavi, Zheming Gao, Lanshan Han, Alvin Lim. Quadratic surface support vector machine with L1 norm regularization. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021046
[16]

Fioralba Cakoni, Pu-Zhao Kow, Jenn-Nan Wang. The interior transmission eigenvalue problem for elastic waves in media with obstacles. Inverse Problems & Imaging, 2021, 15 (3) : 445-474. doi: 10.3934/ipi.2020075
[17]

Yves Capdeboscq, Shaun Chen Yang Ong. Quantitative jacobian determinant bounds for the conductivity equation in high contrast composite media. Discrete & Continuous Dynamical Systems - B, 2020, 25 (10) : 3857-3887. doi: 10.3934/dcdsb.2020228
[18]

Wei Xi Li, Chao Jiang Xu. Subellipticity of some complex vector fields related to the Witten Laplacian. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021047
[19]

Skyler Simmons. Stability of Broucke's isosceles orbit. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3759-3779. doi: 10.3934/dcds.2021015
[20]

Tomáš Roubíček. An energy-conserving time-discretisation scheme for poroelastic media with phase-field fracture emitting waves and heat. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 867-893. doi: 10.3934/dcdss.2017044

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (159)
  • HTML views (0)
  • Cited by (11)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences