Analysis of a model of gambiense sleeping sickness in humans and cattle

References

• R.M. Anderson and R.M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1991.
   Google Scholar
• M. Artzrouni and J.-P. Gouteux, Control strategies for sleeping sickness in Central Africa: a model-based approach, Trop. Med. Int. Health 1(6) (1996), pp. 753–764.
   Google Scholar
• M. Artzrouni and J.-P. Gouteux, A compartmental model of sleeping sickness in central Africa, J. Biol. Syst. 4(4) (1996), pp. 459–477.
   Google Scholar
• D. Bruce, Preliminary Report on the Tsetse Fly Disease Or Nagana, in Zululand, Bennett & Davis, Durban, 1895.
   Google Scholar
• D. Bruce, A. E. Hamerton, H.R. Bateman, and F.P. Mackie, The development of Trypanosoma gambiense in Glossina palpalis, Proc. R. Soc. B: Biol. Sci. 81(550) (1909), pp. 405–414.
   Google Scholar
• A. Castellani, On the discovery of a species of trypanosoma in the cerebrospinal fluid of cases of sleeping sickness, The Lancet 161(4164) (1903), pp. 1735–1736.
   Google Scholar
• K. Chalvet-Monfray, M. Artzrouni, J.-P. Gouteux, P. Auger, and P. Sabatier, A two-patch model of Gambian sleeping sickness: application to vector control strategies in a village and plantations, Acta Biotheor. 46(3) (1998), pp. 207–222.
   Google Scholar
• S. Davis, S. Aksoy, and A. Galvani, A global sensitivity analysis for African sleeping sickness, Parasitology 138 (2011), pp. 516–526.
   Google Scholar
• L. Edelstein-Keshet, Mathematical Models in Biology, McGraw-Hill, New York, 1988 (reprinted by SIAM, Philadelphia, 2003).
   Google Scholar
• J.R. Franco, P.P. Simarro, A. Diarra, and J.G. Jannin, Epidemiology of human African trypanosomiasis, Clinical Epidemiology 6 (2014), pp. 257–275.
   Google Scholar
• H.I. Freedman, S. Ruan, and M. Tang, Uniform persistence and flows near a closed positively invariant set, J. Dyn. Differ. Eq. 6(4) (1994), pp. 583–600.
   Google Scholar
• S. Funk, H. Nishiura, H. Heesterbeek, W. John Edmunds, and F. Checchi, Identifying transmission cycles at the human-animal interface: the role of animal reservoirs in maintaining gambiense human African trypanosomiasis, PLoS Comput. Biol. 9(1) (2013).
   Google Scholar
• J.W. Hargrove, R. Ouifki, D. Kajunguri, G.A. Vale, and S.J. Torr, Modeling the control of trypanosomiasis using trypanocides or insecticide-treated livestock, PLoS Negl. Trop. Dis. 6 (5)(2012), p. e1615.
   Google Scholar
• D. Kajunguri, J.W. Hargrove, R. Oufki, J.Y.T. Mugisha, P.G. Coleman, and S.C. Welburn, Modelling the use of insecticide-treated cattle to control tsetse and Trypanosoma brucei rhodiense in a multi-host population, Bull. Math. Biol. 76 (2014), pp. 673–696.
   Google Scholar
• M.Y. Li, J.R. Graef, L. Wang, and J. Karsai, Global dynamics of a SEIR model with varying total population size, Math. Biosci. 160 (1999), pp. 191–213.
   Google Scholar
• A.K. Lindner and G. Priotto, The unknown risk of vertical transmission in sleeping sickness – a literature review, PLoS Negl. Trop. Dis. 4(12) (2010), p. e783.
   Google Scholar
• G. MacDonald, The Epidemiology and Control of Malaria, Oxford University Press, Oxford, 1957.
   Google Scholar
• T. Madsen, D.I. Wallace, and N. Zupan, Seasonal fluctuation in tsetse fly populations and human African trypanosomiasis: a mathematical model, BIOMAT 2012 (2013), pp. 56–69.
   Google Scholar
• D. Moulay, M.A. Aziz-Alaoui, and M. Cadivel, The chikungunya disease: modeling, vector and transmission global dynamics, Math. Biosci. 229(1) (2011), pp. 50–63.
   Google Scholar
• K.S. Rock, C.M. Stone, I.M. Hastings, M.J. Keeling, S.J. Torr, and N. Chitnis, Mathematical models of human African trypanosomiasis epidemiology, Adv. Parasitol. 87 (2015).
   Google Scholar
• D.J. Rogers, A general model for the African trypanosomiases, Parasitology 97(Pt 1) (1988), pp. 193–212.
   Google Scholar
• R. Ross, The Mathematics of Malaria, Vol. 1, 2nd ed., Murray, London, 1911.
   Google Scholar
• J.A. Rozendaal, Vector control: methods for use by individuals and communities, Tech. Rep., Geneva, 1997.
   Google Scholar
• Z. Shuai and P. van den Driessche, Global stability of infectious disease models using Lyapunov functions, SIAM J. Appl. Math. 73(4) (2013), pp. 1513–1532.
   Google Scholar
• P.P. Simarro, J.R. Franco, A. Diarra, J.A. Ruiz Postigo, and J. Jannin, Diversity of human African trypanosomiasis epidemiological settings requires fine-tuning control strategies to facilitate disease elimination, Res. Rep. Trop. Med. 4 (2013), pp. 1–6.
   Google Scholar
• H.L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge University Press, Cambridge, 1995.
   Google Scholar
• P. Solano, S.J. Torr, and M.J. Lehane, Is vector control needed to eliminate gambiense human african trypanosomiasis?, Front. Cell. Infect. Microbiol. 3(33) (2013).
   Google Scholar
• P. Steinmann, C.M. Stone, C. Simone Sutherland, M. Tanner, and F. Tediosi, Contemporary and emerging strategies for eliminating human African trypanosomiasis due to Trypanosoma brucei gambiense: review, Trop. Med. Int. Health 20(6) (2015), pp. 707–718.
   Google Scholar
• P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), pp. 29–48.
   Google Scholar