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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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In this paper, we aim to construct a nonstandard finite difference (NSFD) scheme to solve numerically a mathematical model for cholera epidemic dynamics. We first show that if the basic reproduction number is less than unity, the disease-free equilibrium (DFE) is locally asymptotically stable. Moreover, we mainly establish the global stability analysis of the DFE and endemic equilibrium by using suitable Lyapunov functionals regardless of the time step size. Finally, numerical simulations with different time step sizes and initial conditions are carried out and comparisons are made with other well-known methods to illustrate the main theoretical results.
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참고문헌 (41)
참고문헌 신청
R. E. Mickens / 1999 / Discretizations of nonlinear differential equations using explicit nonstandard methods / J. Comput. Appl. Math 110(1):181~185
A. K. Misra / 2012 / A delay mathematical model for the spread and control of water borne diseases / J. Theoret. Biol 301:49~56
Z. Mukandavire / 2007 / Sex-structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe / J. Math. Biol 54:669~699
Z. Mukandavire / 2011 / Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe / Proceedings of the National Academy of Sciences of the United States of America 108(21):8767~8772
Y. Muroya / 2012 / Global stability for a discrete epi-demic model for disease with immunity and latency spreading in a heterogeneous host population / Nonlinear Anal. Real World Appl 13(1):258~274
A. K. Misra / 2012 / A delay mathematical model for the spread and control of water borne diseases / J. Theoret. Biol 301:49~56
Z. Mukandavire / 2007 / Sex-structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe / J. Math. Biol 54:669~699
Z. Mukandavire / 2011 / Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe / Proceedings of the National Academy of Sciences of the United States of America 108(21):8767~8772
Y. Muroya / 2012 / Global stability for a discrete epi-demic model for disease with immunity and latency spreading in a heterogeneous host population / Nonlinear Anal. Real World Appl 13(1):258~274
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