An age-structured model for the spread of epidemic cholera: Analysis and simulation

Alexanderian, Alen; Gobbert, Matthias K.; Fister, K. Renee; Gaff, Holly; Lenhart, Suzanne; Schaefer, Elsa

doi:10.1016/j.nonrwa.2011.06.009

Cited by 43 publications

(19 citation statements)

References 44 publications

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“…However, the lack of distinguishability between the individual mechanisms shown here suggests that models combining multiple features may encounter identifiability issues. We also did not evaluate our conclusions outside of the deterministic ODE framework, although partial differential equation (PDE), agent-based, and stochastic models are also frequently used in similar contexts [6, 68, 72, 73]. In addition, most of the parameter values were motivated from a single outbreak dataset (Angola, 2006), and may not reflect the breadth of parameter space for cholera epidemics.…”

Section: Discussionmentioning

confidence: 99%

Model distinguishability and inference robustness in mechanisms of cholera transmission and loss of immunity

Lee

Kelly

Ochocki

et al. 2017

Journal of Theoretical Biology

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Mathematical models of cholera and waterborne disease vary widely in their structures, in terms of transmission pathways, loss of immunity, and a range of other features. These differences can affect model dynamics, with different models potentially yielding different predictions and parameter estimates from the same data. Given the increasing use of mathematical models to inform public health decision-making, it is important to assess model distinguishability (whether models can be distinguished based on fit to data) and inference robustness (whether inferences from the model are robust to realistic variations in model structure). In this paper, we examined the effects of uncertainty in model structure in the context of epidemic cholera, testing a range of models with differences in transmission and loss of immunity structure, based on known features of cholera epidemiology. We fit these models to simulated epidemic and long-term data, as well as data from the 2006 Angola epidemic. We evaluated model distinguishability based on fit to data, and whether the parameter values, model behavior, and forecasting ability can accurately be inferred from incidence data. In general, all models were able to successfully fit to all data sets, both real and simulated, regardless of whether the model generating the simulated data matched the fitted model. However, in the long-term data, the best model fits were achieved when the loss of immunity structures matched those of the model that simulated the data. Two parameters, one representing person-to-person transmission and the other representing the reporting rate, were accurately estimated across all models, while the remaining parameters showed broad variation across the different models and data sets. The basic reproduction number (ℛ0) was often poorly estimated even using the correct model, due to practical unidentifiability issues in the waterborne transmission pathway which were consistent across all models. Forecasting efforts using noisy data were not successful early in the outbreaks, but once the epidemic peak had been achieved, most models were able to capture the downward incidence trajectory with similar accuracy. Forecasting from noise-free data was generally successful for all outbreak stages using any model. Our results suggest that we are unlikely to be able to infer mechanistic details from epidemic case data alone, underscoring the need for broader data collection, such as immunity/serology status, pathogen dose response curves, and environmental pathogen data. Nonetheless, with sufficient data, conclusions from forecasting and some parameter estimates were robust to variations in the model structure, and comparative modeling can help to determine how realistic variations in model structure may affect the conclusions drawn from models and data.

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Section: Discussionmentioning

confidence: 99%

Model distinguishability and inference robustness in mechanisms of cholera transmission and loss of immunity

Lee

Kelly

Ochocki

et al. 2017

Journal of Theoretical Biology

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“…Then, the mathematical theory of the age-structured population dynamics was proposed by Iannelli [19]. Afterwards, more and more epidemic models with age structure were studied in [20][21][22][23][24][25][26][27][28]. Recently, a new age-structured malaria model incorporating the age of latent period and the age of prevention period was formulated by Guo et al [29].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of an Age-Structured SEIRS Model with Time Delay

Yin

2020

Mathematics

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This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results.

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“…Some other models of cholera disease transmission were developed by many researchers. [6][7][8][9][10][11][12] Again, the optimal control is an important tool in mathematics that is extensively used to control a dynamical system. Pontryagin et al 13 developed a method to solve optimal control problems.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Analysis of a Cholera Epidemic Model

Panja

2019

Biophys. Rev. Lett.

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In this paper, a cholera disease transmission mathematical model has been developed. According to the transmission mechanism of cholera disease, total human population has been classified into four subpopulations such as (i) Susceptible human, (ii) Exposed human, (iii) Infected human and (iv) Recovered human. Also, the total bacterial population has been classified into two subpopulations such as (i) Vibrio Cholerae that grows in the infected human intestine and (ii) Vibrio Cholerae in the environment. It is assumed that the cholera disease can be transmitted in a human population through the consumption of contaminated food and water by Vibrio Cholerae bacterium present in the environment. Also, it is assumed that Vibrio Cholerae bacterium is spread in the environment through the vomiting and feces of infected humans. Positivity and boundedness of solutions of our proposed system have been investigated. Equilibrium points and the basic reproduction number [Formula: see text] are evaluated. Local stability conditions of disease-free and endemic equilibrium points have been discussed. A sensitivity analysis has been carried out on the basic reproduction number [Formula: see text]. To eradicate cholera disease from the human population, an optimal control problem has been formulated and solved with the help of Pontryagin’s maximum principle. Here treatment, vaccination and awareness programs have been considered as control parameters to reduce the number of infected humans from cholera disease. Finally, the optimal control and the cost-effectiveness analysis of our proposed model have been performed numerically.

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An age-structured model for the spread of epidemic cholera: Analysis and simulation

Cited by 43 publications

References 44 publications

Model distinguishability and inference robustness in mechanisms of cholera transmission and loss of immunity

Model distinguishability and inference robustness in mechanisms of cholera transmission and loss of immunity

Stability Analysis of an Age-Structured SEIRS Model with Time Delay

Optimal Control Analysis of a Cholera Epidemic Model

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