Abstract
ABSTRACTA new modelling framework is proposed to study the within-host and between-host dynamics of cholera, a severe intestinal infection caused by the bacterium Vibrio cholerae. The within-host dynamics are characterized by the growth of highly infectious vibrios inside the human body. These vibrios shed from humans contribute to the environmental bacterial growth and the transmission of the disease among humans, providing a link from the within-host dynamics at the individual level to the between-host dynamics at the population and environmental level. A fast-slow analysis is conducted based on the two different time scales in our model. In particular, a bifurcation study is performed, and sufficient and necessary conditions are derived that lead to a backward bifurcation in cholera epidemics. Our result regarding the backward bifurcation highlights the challenges in the prevention and control of cholera.
Highlights
Mathematical modelling of infectious diseases has played a significant role in furthering our understanding of disease dynamics and developing effective prevention and control measures against epidemics
To the best of our knowledge, no existing work has attempted to address the coupled within- and between-host dynamics of cholera, despite the fact that a large body of work has been devoted to its population level modelling (e.g. [4,5,6,17,21,22,26,28,29,32,33,34,35,36])
The main contribution of this work is that we have developed a new mathematical modelling framework to study the within- and between-host dynamics of cholera, and this framework can be extended to other infectious diseases with free-living pathogens in the environment
Summary
Mathematical modelling of infectious diseases has played a significant role in furthering our understanding of disease dynamics and developing effective prevention and control measures against epidemics. WANG [17] are constant whereas our model utilizes variable transmission rates, dependent on both the environmental and human vibrios, to explicitly link the fast and slow dynamics. Their cholera study has a major focus on the medical aspects, whereas our work is more mathematically sophisticated.
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