Journal of Applied Mathematics

Mathematical Analysis of Rabies Infection

C. S. Bornaa, Baba Seidu, and M. I. Daabo

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

A mathematical model is proposed to study the dynamics of the transmission of rabies, incorporating predation of dogs by humans. The model is shown to have a unique disease-free equilibrium which is globally asymptotically stable whenever 0 1 . Local sensitivity analysis suggests that the disease can be controlled through reducing contact with infected dogs, increasing immunization of dogs, screening recruited dogs, culling of infected dogs, and use of dog meat as a delicacy.

Article information

Source
J. Appl. Math., Volume 2020 (2020), Article ID 1804270, 17 pages.

Dates
Received: 17 October 2019
Revised: 1 February 2020
Accepted: 3 March 2020
First available in Project Euclid: 14 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.jam/1589421634

Digital Object Identifier
doi:10.1155/2020/1804270

Mathematical Reviews number (MathSciNet)
MR4083299

Citation

Bornaa, C. S.; Seidu, Baba; Daabo, M. I. Mathematical Analysis of Rabies Infection. J. Appl. Math. 2020 (2020), Article ID 1804270, 17 pages. doi:10.1155/2020/1804270. https://projecteuclid.org/euclid.jam/1589421634


Export citation

References

  • D. T. S. Hayman, N. Johnson, D. L. Horton et al., “Evolutionary history of rabies in Ghana,” PLoS Neglected Tropical Diseases, vol. 5, no. 4, Article ID e1001, 2011.
  • World Health Organization, Rabies Fact Sheet, World Health Organization, Geneva, Switzerland, 2016, http://www.who.int/mediacentre/fact-sheets/fs099/en/.
  • C. E. Rupprecht, D. Briggs, C. M. Brown, R. Franka, S. L. Katz, and H. D. Kerretal, Use of A Reduced (4-Dose) Vaccine Schedule for Postexposure Prophylaxis to Prevent Human Rabies: Recommendations of the Advisory Committee on Immunization Practices, Department of Health and Human Services, Centers for Disease Control and Prevention, Atlanta, GA, USA, 2010.
  • P. A. K. Addy, “Epidemiology of rabies in Ghana,” in Rabies in the Tropics, E. Kuwert, C. Merieux, H. Koprowski, and K. Bogel, Eds., Springer, Berlin, Germany, 1985.
  • J. K. K. Asamoah, F. T. Oduro, E. Bonyah, and B. Seidu, “Modelling of rabies transmission dynamics using optimal control analysis,” Journal of Applied Mathematics, vol. 2017, Article ID 2451237, 23 pages, 2017.
  • C. S. Bornaa, O. D. Makinde, and I. Y. Sieni, “Eco-epidemiological model and optimal control of disease transmission between humans and animals,” Communications in Mathematical Biology and Neuroscience, vol. 2015, p. 26, 2015.
  • C. S. Bornaa, I. Y. Sieni, and B. Seidu, “Modelling zoonotic diseases with treatment in both human and animal populations,” Communications in Mathematical Biology and Neuroscience, vol. 2017, p. 11, 2017.
  • H. Joshi, S. Lenhart, K. Albright, and K. Gipson, “Modeling the effect of information campaign on the HIV epidemic in Uganda,” Mathematical Biosciences and Engineering, vol. 5, no. 4, pp. 757–770, 2008.
  • H. Gaff and E. Schaefer, “Optimal control applied to vaccination and treatment strategies for various epidemiological models,” Mathematical Biosciences and Engineering, vol. 6, no. 3, pp. 469–492, 2009.
  • M. Kgosimore and E. Lungu, “The effects of vertical transmission on the spread of HIV/AIDS in the presence of treatment,” Mathematical Biosciences and Engineering, vol. 3, no. 2, pp. 297–312, 2006.
  • Z. Mukandavire and W. Garira, “Sex-structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe,” Journal of Mathematical Biology, vol. 54, no. 5, pp. 669–699, 2007.
  • Q. Hou, Z. Jin, and S. Ruan, “Dynamics of rabies epidemics and the impact of control efforts in Guangdong Province, China,” Journal of Theoretical Biology, vol. 300, pp. 39–47, 2012.
  • R. Naresh, A. Tripathi, and S. Omar, “Modelling the spread of AIDS epidemic with vertical transmission,” Applied Mathematics and Computation, vol. 178, no. 2, pp. 262–272, 2006.
  • R. Granish, C. Gilks, C. Dye, K. M. De Cock, and B. G. Williams, “Universal voluntary HIV testing with immediate antiretroviral therapy as a strategy for elimination of HIV transmission:a mathematical model,” The Lancet, vol. 373, no. 9657, pp. 48–57, 2008.
  • B. Seidu, O. D. Makinde, and I. Y. Seini, “Mathematical analysis of the effects of HIV-malaria co-infection on workplace productivity,” Acta Biotheoretica, vol. 63, no. 2, pp. 151–182, 2015.
  • Y.-H. Hsieh and S.-P. Sheu, “The effect of density-dependent treatment and behavior change on the dynamics of HIV transmission,” Journal of Mathematical Biology, vol. 43, no. 1, pp. 69–80, 2001.
  • Y. Jin, W. Wang, and S. Xiao, “An SIRS model with a nonlinear incidence rate,” Chaos, Solitons & Fractals, vol. 34, no. 5, pp. 1482–1497, 2007.
  • B. Seidu and O. D. Makinde, “Optimal control of HIV/AIDS in the workplace in the presence of careless individuals,” Computational and Mathematical Methods in Medicine, vol. 2014, Article ID 831506, 19 pages, 2014.
  • X. Wang and J. Lou, “Two dynamic models about rabies between dogs and human,” Journal of Biological Systems, vol. 16, no. 4, pp. 519–529, 2008.
  • M. J. Carroll, A. Singer, G. C. Smith, D. P. Cowan, and G. Massei, “The use of immunocontraception to improve rabies eradication in urban dog populations,” Wildlife Research, vol. 37, no. 8, pp. 676–687, 2010.
  • W. Ding, L. J. Gross, K. Langston, S. Lenhart, and L. A. Real, “Rabies in raccoons: optimal control for a discrete time model on a spatial grid,” Journal of Biological Dynamics, vol. 1, no. 4, pp. 379–393, 2007.
  • O. Diekmann, J. A. P. Heesterbeek, and M. G. Roberts, “The construction of next-generation matrices for compartmental epidemic models,” Journal of The Royal Society Interface, vol. 7, no. 47, pp. 873–885, 2010.
  • C. Castillo-Chavez, Z. L. Feng, and W. Z. Huang, “On the computation ${\mathrm{\mathcal{R}}}_{0}$ and its role on global stability,” IMA Journal of Applied Mathematics, vol. 125, pp. 229–250, 1992.
  • S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology,” Journal of Theoretical Biology, vol. 254, no. 1, pp. 178–196, 2008.
  • C. Castillo-Chavez and S. Baojun, “Dynamical models of tuberculosis and their applications,” Mathematical Biosciences and Engineering, vol. 1, no. 2, pp. 361–404, 2004. \endinput