Analysis of Cholera model with treatment noncompliance

[1] JR. Andrews and S. Basu, Transmission dynamics and control of cholera in Haiti: an epidemic model, The Lancet 377 (2011) 1248-1255.

[2] P. Ana, L Paiao, JS. Christiana and FMT Del_m, A cholera mathematical model with vaccination and the biggest outbreak of world's history, Retrieved from http: \\www:aimspress:com=journal=Math, (2018).

[3] PR. Brayton, ML. Tamplin, & RR. Colwell, Enumeration of vibrio cholerae in Bangladesh waters by fluorescent-antibody direct viable count Appl. Environ.Microbiol. 53 (1987) 2862-2865.

[4] V. Capasso and SL. Paveri-Fontana, A mathematical model for the 1973 cholera epidemic in the European, Mediterranean region, Rev.Epidemiol. Sante. 27 (1979) 121-132.

[5] F. Capone, V. De Cataldis and R. De Luca, Inuence of di_usion on the stability of equilibria in a reaction-diffusion system modeling cholera dynamic, J. Math. Biol. 71 (2008) 1107-1131.

[6] C. Codeco, Endemic and epidemic dynamic of cholera: the role of the aquatic reservoir, BMC Infectious Diseases (2001)

[7] Y. Chayu and W. Jin, A cholera transmission model incorporating the impact of medical resources, Mathematical Biosciences and Engineering 16(5) (2019) 5226-5246.

[8] JK. Hale. Ordinary di_erential equations, John Wiley, 1969.

[9] DM. Hartley, JB. Morris, DL. Smith, Hyperinfectivity: a critical element in the ability of V. cholerae to cause epidemics? Plos Med. 3(1) (2006) e7.

[10] MW. Hirsch, Systems of di_erential equations that are competitive or cooperative IV. Structural stability in 3-dimensional systems, Journal of Di_erential Equations. 80 (1989) 94-106.

[11] AE. Kamuhanda, O. Shaibu and W. Mary, Mathematical modeling and analysis of the dynamics of cholera, Global Journal of Pure and Applied Mathematics. 14(9) (2018) 1259-1275.

[12] AA., King, E.L. Ionides, M. Pascual & M.J. Bouma, Inapparent infections and cholera dynamics. Emerging Infectious Diseases. 14 (2008) 877-881.

[13] JB. Kaper, JG. Morris Jr., & MM. Levine, Clin. Microbiol. Rev. (1995) 48-86.

[14] JP. Lasalle, The stability of dynamical systems. Philadelphia, PA: SIAM, 1976.

[15] AP. Lemos-Paiao, CJ. Silva and DFM Torres An epidemic model for cholera with optimal control treatment, J. Comput. Appl. Math. 318 (2017) 168-180.

[16] MY. Li and JS. Muldowney, A geometric approach to global stability problems, SIAM J.Math.Anal. 27 (1996) 1070-1083.

[17] MY. Li and JS. Muldowney, Global stability for the SEIR model in epidemiology, Mathematical Biosciences 125 (1995) 155-164.

[18] JS. Mulodowney, Compound matrices and ordinary differential equations, Rocky Mountain Journal of Mathematics 20 (1990) 857-872

[19] Z. Mukandavire, S. Liao, J. Wang, H. Ga_, DL. Smith and JG. Morris, Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe, Proc. Natl Acad. Sci. 108 (2011) 8767-8772.

[20] RLM. Neilan, E. Schaefer, H. Ga_, KR. Fister and S. Lenhart, Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe, Proc. Natl Acad. Sci. 108 (2011) 8767-8772.

[21] CC. Obiora and JD. Kelvin, Analysis and optimal control intervention strategies of a waterborne disease model:a realistic case study, Hindawi Journal of Applied Mathematics 14 (2018)

[22] M. Pascual, MJ. Bouma, AP. Dopson, Cholera and climate: revisiting the quantitative evidence, Microbes and Infection 4(2) (2002) 237-245.

[23] HL. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, mathematical survey and monographs, American Mathematical Society (1995) 231-240

[24] HL. Smith, Systems of di_erential equations which generate an order preserving ow, SIAM Review 30 (1988) 87-113.

[25] RP. Sanches, CP. Ferreira and RA. Kraenkel, The role of immunity and seasonality in cholera epidemics, Bulletin of Mathematical Biology 73(12) (2011) 2916-2931.

[26] J. Sepulveda, H. Gomez-Dantes, M. Bronfman, Cholera in the Americas: an overview. Infection 20(5) (1992) 243-248.

[27] J. Tumwiine, JYT. Mugisha and LS. Luboobi, A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity, Applied Mathematics and Computation 189 (2007) 1953-1965.

[28] JH. Tien and DJ. Earn, Multiple transmission pathways and disease dynamics in a waterborne pathogen model, Bulletin of Mathematical Biology 72(6) (2010) 1506-1533.

[29] World Health Organization web page: www.who.org. (2014)

[30] T. Xiaohong, X. Rui and L. Jiazche, Mathematical analysis of a cholera infection model with vaccination strategy, Applied Mathematics and Computation 361 (2019) 517-535.