Desirable Dog-Rabies Control Methods in an Urban setting in Africa -a Mathematical Model

Desirable Dog-Rabies Control Methods in an Urban setting in Africa -a Mathematical Model

Автор: Edwiga Kishinda Renald, Dmitry Kuznetsov, Katharina Kreppel

Журнал: International Journal of Mathematical Sciences and Computing @ijmsc

Статья в выпуске: 1 vol.6, 2020 года.

Бесплатный доступ

Rabies is a fatal, zoonotic, viral disease that causes an acute inflammation of the brain in humans and other mammals. It is transmitted through contact with bodily fluids of infected mammals, usually via bites or scratches. In this paper, we formulate a deterministic model which measures the effects of different rabies control methods (mass-culling and vaccination of dogs) for urban areas near wildlife, using the Arusha region in Tanzania as an example. Values for various parameters were deduced from five years’ worth of survey data on Arusha’s dog population. Data included vaccination coverage, dog bites and rabies deaths recorded by a local non-governmental organization and the Ministry of Agriculture, Livestock Development and Fisheries of the United Republic of Tanzania. The basic reproduction number R_0 and effective reproduction number Re were computed and found to be 1.9 and 1.2 respectively. These imply that the disease is endemic in Arusha. The numerical simulation of the reproduction number shows that vaccination is the most appropriate control method for rabies transmission in urban areas near wildlife reservoirs. The disease free equilibrium ε_0 is also computed. If the effective reproduction number R_e is computed and found to be less than 1, it implies that it is globally asymptotically stable in the feasible region Φ. If R_e> 1 it is implied that there is one equilibrium point which is endemic and it is locally asymptotically stable.

Еще

Rabies, Vaccination, Culling for Dog Control, SEIV-Model, Reproduction Number, Arusha

Короткий адрес: https://sciup.org/15017137

IDR: 15017137   |   DOI: 10.5815/ijmsc.2020.01.05

Список литературы Desirable Dog-Rabies Control Methods in an Urban setting in Africa -a Mathematical Model

  • Abta, A., Laarabi, H., and Talibi Alaoui, H. (2014). The hopf bifurcation analysis and optimal control of a delayed sir epidemic model.International Journal of Analysis, 2014.
  • Addo, K. M. (2012). An SEIR Mathematical Model for dog Rabies; Case Study: Bongo District, Ghana. PhD thesis.
  • Allen, L. J. and Van den Driessche, P. (2008). The basic reproduction number in some discrete-time epidemic models. Journal of Difference Equations and Applications, 14(10-11):1127–1147.
  • Amaku, M., Dias, R. A., and Ferreira, F. (2010). Dynamics and control of stray dog populations. Mathematical Population Studies, 17(2):69–78.
  • Aweya, J., Ouellette, M., and Montuno, D. Y. (2004). Design and stability analysis of a rate control algorithm using the routh-hurwitz stability criterion. IEEE/ACM transactions on networking, 12(4):719 732.
  • Cintr´on-Arias, A., Castillo-Ch´avez, C., Bettencourt, L. M., Lloyd, A. L., and Banks, H. (2009). The estimation of the effective reproductive number from disease outbreak data. Math BiosciEng, 6(2):261–282.
  • Cowling, B. J., Lau, M. S., Ho, L.-M., Chuang, S.-K., Tsang, T., Liu, S.-H., Leung, P.-Y., Lo, S.-V., and Lau, E. H. (2010). The effective reproduction number of pandemic influenza: prospective estimation. Epidemiology (Cambridge, Mass.), 21(6):842.
  • Ega, T. T., Luboobi, L. S., and Kuznetsov, D. (2015). Modeling the dynamics of rabies transmission with vaccination and stability analysis. Applied and Computational Mathematics, 4(6):409–419.
  • El-Marhomy, A. A. and Abdel-Sattar, N. E. (2004). Stability analysis of rotor-bearing systems via routh-hurwitz criterion.Applied Energy, 77(3):287–308.
  • Gil, J. J., Avello, A., Rubio, A., and Florez, J. (2004). Stability analysis of a 1 dof haptic interface using the routh-hurwitz criterion. IEEE transactions on control systems technology, 12(4):583–588.
  • Hampson, K., Dushoff, J., Cleaveland, S., Haydon, D. T., Kaare, M., Packer, C., and Dobson, A. (2009). Transmission dynamics and prospects for the elimination of canine rabies. PLoS biology, 7(3):e1000053.
  • Hou, Q., Jin, Z., and Ruan, S. (2012). Dynamics of rabies epidemics and the impact of control efforts in guangdong province, china. Journal of theoretical biology, 300:39–47.
  • Iggidr, A., Mbang, J., Sallet, G., and Tewa, J.-J. (2007). Multi-compartment models. Discrete and Continuous Dynamical Systems-Series S, 2007(Special):506–519.
  • Knobel, D. L., Cleaveland, S., Coleman, P. G., F`evre, E. M., Meltzer, M. I., Miranda, M. E. G., Shaw, A., Zinsstag, J., and Meslin, F.-X. (2005). Re-evaluating the burden of rabies in Africa and Asia. Bulletin of the World health Organization, 83:360–368.
  • L´echenne, M., Oussiguere, A., Naissengar, K., Mindekem, R., Mosimann, L., Rives, G., Hattendorf, J., Moto, D. D., Alfaroukh, I. O., Zinsstag, J., et al. (2016). Operational performance and analysis of two rabies vaccination campaigns in ndjamena, chad. Vaccine, 34(4):571–577.
  • Lembo, T., Hampson, K., Kaare, M. T., Ernest, E., Knobel, D., Kazwala, R. R., Haydon, D. T., and Cleaveland, S. (2010). The feasibility of canine rabies elimination in Africa: dispelling doubts with data. PLoS neglected tropical diseases, 4(2):e626.
  • Leung, T. and Davis, S. A. (2017). Rabies vaccination targets for stray dog populations. Frontiers in veterinary science, 4:52.
  • Morters, M. K., Restif, O., Hampson, K., Cleaveland, S., Wood, J. L., and Conlan, A. J. (2013). Evidence-based control of canine rabies: a critical review of population density reduction. Journal of animal ecology, 82(1):6–14.
  • Mpolya, E. A., Lembo, T., Lushasi, K., Mancy, R., Mbunda, E. M., Makungu, S., Maziku, M., Sikana, L., Jaswant, G., Townsend, S., et al. (2017). Toward elimination of dog-mediated human rabies: experiences from implementing a large-scale demonstration project in southern Tanzania. Frontiers in veterinary science, 4:21.
  • Paul, M., Majumder, S. S., Sau, S., Nandi, A. K., and Bhadra, A. (2016). High early life mortality in free-ranging dogs is largely influenced by humans. Scientific reports, 6:19641.
  • Sambo, M., Cleaveland, S., Ferguson, H., Lembo, T., Simon, C., Urassa, H., and Hampson, K. (2013). The burden of rabies in Tanzania and its impact on local communities. PLoS neglected tropical diseases, 7(11):e2510.
  • Totton, S. C.,Wandeler, A. I., Zinsstag, J., Bauch, C. T., Ribble, C. S., Rosatte, R. C., and McEwen, S. A. (2010). Stray dog population demographics in Jodhpur, India following a population control/rabies vaccination program. Preventive veterinary medicine, 97(1):51–57.
  • Tulu, A. M. and Koya, P. R. (2017). The impact of infective immigrants on the spread of dog rabies. American Journal of Applied Mathematics, 5(3):68.
  • Van den Driessche, P. and Watmough, J. (2008).Further notes on the basic reproduction number. In Mathematical epidemiology, pages 159–178. Springer.
  • Zhang, J., Jin, Z., Sun, G.-Q., Zhou, T., and Ruan, S. (2011). Analysis of rabies in china: transmission dynamics and control. PLoS one, 6(7):e20891.
  • Zinsstag, J., D¨urr, S., Penny, M., Mindekem, R., Roth, F., Gonzalez, S. M., Naissengar, S., and Hattendorf, J. (2009). Transmission dynamics and economics of rabies control in dogs and humans in an African city. Proceedings of the National Academy of Sciences, 106(35):14996–15001.
  • P. van den Driessche, J. Watmough, A simple sis epidemic model with a backward bifurcation, Journal of Mathematical Biology 40 (2000) 525–540.
Еще
Статья научная
QR-код для установки приложения SciUp Наведите камеру и скачайте бесплатное приложение SciUp