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Mathematical Models in Epidemiology pp 229–245Cite as

Models for Diseases Transmitted by Vectors

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Part of the book series: Texts in Applied Mathematics ((TAM,volume 69))

Abstract

Many diseases are transmitted from human to human indirectly, through a vector. Vectors are living organisms that can transmit infectious diseases between humans. Many vectors are bloodsucking insects that ingest disease-producing microorganisms during blood meals from an infected (human) host, and then inject it into a new host during a subsequent blood meal. The best known vectors are mosquitoes for diseases including malaria, dengue fever, chikungunya, Zika virus, Rift Valley fever, yellow fever, Japanese encephalitis, lymphatic filariasis, and West Nile fever, but ticks (for Lyme disease and tularemia), bugs (for Chagas’ disease), flies (for onchocerciasis), sandflies (for leishmaniasis), fleas (for plague, transmitted by fleas from rats to humans), and some freshwater snails (for schistosomiasis) are vectors for some diseases.

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References

  1. Brauer, F. (2017) A final size relation for epidemic models of vector - transmitted diseases, Infectious Disease Modelling, 2: 12–20.

    Article  Google Scholar 

  2. Brauer, F. (2019) A singular perturbation approach to epidemics of vector-transmitted diseases, to appear.

    Google Scholar 

  3. Brauer, F. and C. Kribs (2016) Dynamical Systems for Biological Modeling: An Introduction, CRC Press.

    MATH  Google Scholar 

  4. Chowell, G., P. Diaz-Duenas, J.C. Miller, A. Alcazar-Velasco, J.M. Hyman, P.W. Fenimore, and C. Castillo-Chavez (2007) Estimation of the reproduction number of dengue fever from spatial epidemic data, Math. Biosc. 208: 571–589.

    Article  MathSciNet  Google Scholar 

  5. Coffeng, L.E., W.A. Stolk, HGM Zouré, J.L. Vetterman, & K.B. Agblewonu (2013) African programme for onchocerciasis control 1995–2015:Model-estimated health impact and cost, PLoS Neglected tropical diseases, 7: e2032. https://doi.org/10.13571/journal.ptnd.0002032.

    Article  Google Scholar 

  6. Cushing, J.M. & O. Diekmann (2016) The many guises of \(\mathcal {R}_0\) (a didactic note), J. Theor. Biol. 404: 295–302.

    Article  Google Scholar 

  7. Dietz, K. (1982) The population dynamics of onchocerciasis, in Population Dynamics of Infectious Diseases (R.m. Anderson, ed.), Chapman and Hall, London, pp.209–241.

    Chapter  Google Scholar 

  8. Hopkins, A. and B.A. Boatin (2011) Onchocerciasis, water and sanitation-related diseases and the environment: Challenges, interventions, and preventive measures (J.M.H. Selendi, ed.), John Wiley and Sons: pp.133–149.

    Google Scholar 

  9. Hoppensteadt, F.C. (1966) Singular perturbations on the infinite interval, Trans. Amer. Math. Soc. 123: 521–535.

    Article  MathSciNet  Google Scholar 

  10. Kucharski, A.J., S. Funk, R.M. Egge, H-P. Mallet, W.J. Edmunds and E.J. Nilles (2016) Transmission dynamics of Zika virus in island populations: a modelling analysis of the 2013–14 French Polynesia outbreak, PLOS Neglected tropical Diseases DOI 101371

    Google Scholar 

  11. Ledder, G., D. Sylvester, R.R. Bouchat, and J.A. Thiel (2017) Continued and pulsed epidemiological models for onchocerciasis with implications for eradication strategy, Math. Biosc. & Eng., to appear.

    Google Scholar 

  12. Levinson, N. (1950) Perturbations of discontinuous solutions of nonlinear systems of differential equations, Acta Math. 82: 71–106.

    Article  MathSciNet  Google Scholar 

  13. Pinho, S.T.R., C.P. Ferreira, L. Esteva, F.R.Barreto, V.C. Morato e Silva and M.G.L Teixeira (2010) Modelling the dynamics of dengue real epidemics, Phil. Trans. Roy. Soc. A 368: 5679–5693.

    Google Scholar 

  14. Plaisier,A.P., E.S. Alley, B.A. Boutin, G.J. van Oortmasrssen, & H. Remme (1995) Irreversible effects of ivermectin on adult parasites in onchocerciasis patients in the onchocerciasis control programme in West Africa, J. Inf. Diseases 172; 204–210.

    Article  Google Scholar 

  15. Rocha, F., M. Aguiar, M. Souza, & N. Stollenwerk (2013) Time-scale separation and centre manifold analysis describing vector-borne disease dynamics, Int. J. Comp. Math 90: 2105–2125.

    MATH  Google Scholar 

  16. Ross, R. (1911) The Prevention of Malaria, 2nd ed., (with Addendum), John Murray, London.

    Google Scholar 

  17. Segel, L.A. & M. Slemrod (1989) The quasi-steady-state assumption: A case study in perturbation, SIAM Review 31: 446–477.

    Article  MathSciNet  Google Scholar 

  18. Souza, M.O. (2014) Multiscale analysis for a vector-borne epidemic model (2014) J. Math. Biol. 68: 1269–1291.

    Article  MathSciNet  Google Scholar 

  19. Takeuchi, Y., W. Ma, & E. Beretta (2000) Global asymptotic properties of a delay SIR epidemic model with finite incubation times, Nonlin. Analysis 42; 931–947.

    MathSciNet  MATH  Google Scholar 

  20. Tihonov, A.N. (1948) On the dependence of the solutions of differential equations on a small parameter, Mat. Sbornik NS 22; 193–204.

    Google Scholar 

  21. van den Driessche, P. and J. Watmough (2002) Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosc. 180:29–48.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, BC, Canada

    Fred Brauer

  2. Mathematical and Computational Modeling Center (MCMSC), Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, USA

    Carlos Castillo-Chavez

  3. Department of Mathematics, Purdue University, West Lafayette, IN, USA

    Zhilan Feng

Authors
  1. Fred Brauer
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  2. Carlos Castillo-Chavez
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  3. Zhilan Feng
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Brauer, F., Castillo-Chavez, C., Feng, Z. (2019). Models for Diseases Transmitted by Vectors. In: Mathematical Models in Epidemiology. Texts in Applied Mathematics, vol 69. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9828-9_6

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