TY - JOUR
T1 - Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model
AU - Yamazaki, Kazuo
AU - Wang, Xueying
PY - 2016/6
Y1 - 2016/6
N2 - In this paper, we study the initial boundary value problem of a reaction-convection-diffusion epidemic model for cholera dynamics, which was developed in [38], named susceptible-infected-recovered-susceptible-bacteria (SIRS-B) epidemic PDE model. First, a local well-posedness result relying on the theory of cooperative dynamics systems is obtained. Via a priori estimates making use of the special structure of the system and continuation of local theory argument, we show that in fact this problem is globally well-posed. Secondly, we analyze the local asymptotic stability of the solutions based on the basic reproduction number associated with this model.
AB - In this paper, we study the initial boundary value problem of a reaction-convection-diffusion epidemic model for cholera dynamics, which was developed in [38], named susceptible-infected-recovered-susceptible-bacteria (SIRS-B) epidemic PDE model. First, a local well-posedness result relying on the theory of cooperative dynamics systems is obtained. Via a priori estimates making use of the special structure of the system and continuation of local theory argument, we show that in fact this problem is globally well-posed. Secondly, we analyze the local asymptotic stability of the solutions based on the basic reproduction number associated with this model.
KW - Cholera dynamics
KW - Disease threshold dynamics
KW - Principal eigenvalues
KW - Stability
KW - The basic reproduction number
KW - Well-posedness
UR - http://www.scopus.com/inward/record.url?scp=84962767276&partnerID=8YFLogxK
U2 - 10.3934/dcdsb.2016.21.1297
DO - 10.3934/dcdsb.2016.21.1297
M3 - Article
AN - SCOPUS:84962767276
SN - 1531-3492
VL - 21
SP - 1297
EP - 1316
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
IS - 4
ER -