TY - JOUR
T1 - Modeling and Analysis of the Multiannual Cholera Outbreaks with Host-Pathogen Encounters
AU - Zhang, Wenjing
N1 - Publisher Copyright:
© 2020 World Scientific Publishing Company.
PY - 2020/6/30
Y1 - 2020/6/30
N2 - Re-emergence of cholera threatens people's health globally. However, its periodic re-emerging outbreaks are still poorly understood. In this paper, we develop a simple ordinary differential equation (ODE) model to study the cholera outbreak cycles. Our model involves both direct (i.e. human-to-human) and indirect (i.e. environment-to-human) transmission routes, due to the multiple interactions between the human host, the pathogen, and the environment. In particular, we model the pathogen searching distance as a Poisson point process, and then formulate the host-pathogen encounter (HPE) rate. A thorough mathematical analysis is performed to investigate local and global dynamics of the model. Necessary and sufficient condition under which the backward bifurcation occurs is derived. Fold, Hopf, and Bogdanov-Takens bifurcations are studied with original model parameter values to reveal their relations with model behaviors. One- and two-dimensional bifurcation diagrams are provided to categorize model dynamics with respect to its parameter values. Analytical and numerical analyses show that our simple model is sufficient to exhibit complex epidemic patterns of cholera dynamics including bistability and annual and multiannual periodic outbreaks. Our result regarding the backward bifurcation and complex dynamics of cholera epidemics highlight the challenges in the prevention and control of the disease.
AB - Re-emergence of cholera threatens people's health globally. However, its periodic re-emerging outbreaks are still poorly understood. In this paper, we develop a simple ordinary differential equation (ODE) model to study the cholera outbreak cycles. Our model involves both direct (i.e. human-to-human) and indirect (i.e. environment-to-human) transmission routes, due to the multiple interactions between the human host, the pathogen, and the environment. In particular, we model the pathogen searching distance as a Poisson point process, and then formulate the host-pathogen encounter (HPE) rate. A thorough mathematical analysis is performed to investigate local and global dynamics of the model. Necessary and sufficient condition under which the backward bifurcation occurs is derived. Fold, Hopf, and Bogdanov-Takens bifurcations are studied with original model parameter values to reveal their relations with model behaviors. One- and two-dimensional bifurcation diagrams are provided to categorize model dynamics with respect to its parameter values. Analytical and numerical analyses show that our simple model is sufficient to exhibit complex epidemic patterns of cholera dynamics including bistability and annual and multiannual periodic outbreaks. Our result regarding the backward bifurcation and complex dynamics of cholera epidemics highlight the challenges in the prevention and control of the disease.
KW - Periodic outbreak of cholera
KW - Poisson point process
KW - bifurcation theory
KW - global stability
UR - http://www.scopus.com/inward/record.url?scp=85092320926&partnerID=8YFLogxK
U2 - 10.1142/S0218127420501205
DO - 10.1142/S0218127420501205
M3 - Article
AN - SCOPUS:85092320926
VL - 30
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
SN - 0218-1274
IS - 8
M1 - 2050120
ER -