Steady State Stability Analysis of a Chagas Disease Model

作者: Daniel James Coffield Jr. , Anna Maria Spagnuolo

DOI: 10.11145/J.BIOMATH.2014.05.261

关键词:

摘要: Chagas disease is caused by the parasite Trypanosoma cruzi , which spread primarily domestic vectors in reduviid family. This work presents a model of dynamics rural village. The consists nonlinear delay logistic-type differential equation for population total and three equations populations infected vectors, humans, mammals. Steady state solutions are derived analyzed. Stability numbers provided with necessary sufficient conditions local asymptotic stability partial results global stability. Numerical simulation presented, verifying theoretical .

参考文章(27)
Linda J. S. Allen, An introduction to mathematical biology ,(2006)
Joel E Cohen, Ricardo E Gurtler, Modeling Household Transmission of American Trypanosomiasis Science. ,vol. 293, pp. 694- 698 ,(2001) , 10.1126/SCIENCE.1060638
Alternative transmission modes for Trypanosoma cruzi. Mathematical Biosciences and Engineering. ,vol. 7, pp. 657- 673 ,(2010) , 10.3934/MBE.2010.7.657
Chris J. Schofield, Jean Jannin, Roberto Salvatella, The future of Chagas disease control Trends in Parasitology. ,vol. 22, pp. 583- 588 ,(2006) , 10.1016/J.PT.2006.09.011
Kenneth Lloyd Cooke, Richard Ernest Bellman, Differential-Difference Equations ,(2012)
Christopher Kribs-Zaleta, Estimating Contact Process Saturation in Sylvatic Transmission of Trypanosoma cruzi in the United States PLoS Neglected Tropical Diseases. ,vol. 4, pp. e656- ,(2010) , 10.1371/JOURNAL.PNTD.0000656
L.A. Ceballos, G.M. Vazquez-Prokopec, M.C. Cecere, P.L. Marcet, R.E. Gürtler, Feeding rates, nutritional status and flight dispersal potential of peridomestic populations of Triatomainfestans in rural northwestern Argentina. Acta Tropica. ,vol. 95, pp. 149- 159 ,(2005) , 10.1016/J.ACTATROPICA.2005.05.010
Nisha Garg, Vandanajay Bhatia, Current status and future prospects for a vaccine against American trypanosomiasis. Expert Review of Vaccines. ,vol. 4, pp. 867- 880 ,(2005) , 10.1586/14760584.4.6.867
Anna Maria Spagnuolo, Meir Shillor, Lindsey Kingsland, Andrea Thatcher, Matthew Toeniskoetter, Benjamin Wood, A logistic delay differential equation model for Chagas disease with interrupted spraying schedules Journal of Biological Dynamics. ,vol. 6, pp. 377- 394 ,(2012) , 10.1080/17513758.2011.587896
AC Silveira, MC Vinhaes, Elimination of vector-borne transmission of Chagas disease Memorias Do Instituto Oswaldo Cruz. ,vol. 94, pp. 405- 411 ,(1999) , 10.1590/S0074-02761999000700080