Global Dynamics for an Age-Structured Cholera Infection Model with General Infection Rates

Jiang, Xin

doi:10.3390/math9232993

Cited by 2 publications

(3 citation statements)

References 37 publications

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“…Velocity-jump processes are close to age structured models, as both consist of a transport equation with a nonlocal term. This nonlocal term, however, is focused at age 0 in age-structured models (the boundary condition-which can be newborns or new infections in other cases-addresses age zero, see, e.g., [20,21])), but is distributed over all states in velocity-jump processes. On that, velocity-jump processes are often more complex to analyze [33,36].…”

Section: Discussionmentioning

confidence: 99%

“…The disease, as a severe public health threat, has been targeted by the modeling community for a long time. Population-level models for the infection have been advanced in [1,[17][18][19], some of which structure the population according to the age [20,21]. A multi-scale model for the disease proposed in [22] makes use of the interaction between the environmental vibrios and human vibrios (inside the body) to link the within-and between-host dynamics.…”

Section: Introductionmentioning

confidence: 99%

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A Multi-Scale Model for Cholera Outbreaks

2022

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Cholera, caused by the pathogenic Vibrio cholerae bacteria, remains a severe public health threat. Although a lot of emphasis has been placed on the population-level spread of the disease, the infection itself starts within the body. As such, we formulated a multi-scale model that explicitly connects the within-host and between-host dynamics of the disease. To model the within-host dynamics, we assigned each susceptible individual with a pathogen load that increases through the uptake of contaminated food and water (booster event). We introduced minimal and maximal times when the booster events happen and defined a time since the last booster event. We then scaled the within-host dynamics to the population where we structured the susceptible population using the two variables (pathogen load and time since the last booster event). We analyzed the pathogen load’s invariant distribution and utilized the results and time scale assumptions to reduce the dimension of the multi-scale model. The resulting model is an SIR model whose incidence function has terms derived from the multi-scale model. We finally conducted numerical simulations to investigate the long-term behavior of the SIR model. The simulations revealed parameter regions where either no cholera cases happen, where cholera is present at a low prevalence, and where a full-blown cholera epidemic takes off.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Multi-Scale Model for Cholera Outbreaks

2022

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“…By incorporating age structures and overall infection rates into a cholera model, Jiang [12] examined the model's global dynamics, the existence and point dissipativeness of the orbit and asymptotical smoothness. Next, they focus on the existence and local stability of equilibria and also discuss uniform persistence, followed by numerical simulations.…”

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confidence: 99%