Disease X epidemic control using a stochastic model and a deterministic approximation: Performance comparison with and without parameter uncertainties

BACKGROUND

The spread of infectious diseases can be modeled using deterministic or stochastic models. A deterministic approximation of a stochastic model can be appropriate under some conditions, but is unable to capture the discrete nature of populations. We look into the choice of a model from the perspective of decision making.

METHOD

We consider an emerging disease (Disease X) in a closed population modeled by a stochastic SIR model or its deterministic approximation. The objective of the decision maker is to minimize the cumulative number of symptomatic infected-days over the course of the epidemic by picking a vaccination policy. We consider four decision making scenarios: based on the stochastic model or the deterministic model, and with or without parameter uncertainty. We also consider different sample sizes for uncertain parameter draws and stochastic model runs. We estimate the average performance of decision making in each scenario and for each sample size.

RESULTS

The model used for decision making has an influence on the picked policies. The best achievable performance is obtained with the stochastic model, knowing parameter values, and for a large sample size. For small sample sizes, the deterministic model can outperform the stochastic model due to stochastic effects. Resolving uncertainties may bring more benefit than switching to the stochastic model in our example.

CONCLUSION

This article illustrates the interplay between the choice of a type of model, parameter uncertainties, and sample sizes. It points to issues to be considered when optimizing a stochastic model.

A Simplified Consistent Nonlinear Mild-Slope Equation Model for Random Waves Propagation and Dissipation

The model for ocean surface wave propagation can be formulated either in the form of deterministic models or stochastic models. The stochastic models appear to be particularly attractive in the global domain due to their computational efficiency. However, in the nearshore region, the phase becomes highly correlated, and the phase information therefore becomes critical. Therefore, a simplified consistent nonlinear mild-slope equation model has been developed in order to take advantage of the deterministic model for handling phase information, as well as the stochastic model for numerical simplicity. We demonstrate the advanced performance of the present model for random waves by comparing it with laboratory data and previous models.

Innovation of flux chamber network design for surface methane emission from landfills using spatial interpolation models

Solid waste landfills are one of the primary anthropogenic sources of methane emissions which are often estimated by flux chamber measurements on landfill surfaces. Due to the small footprint of the flux chamber on the surface coverage, however, it is important to design a proper spatial deployment of the chambers with an optimal number of measurement points such that the measured fluxes are correctly scaled up to the whole landfill area. In order to improve the design of flux chamber network, several deterministic interpolation models were applied and results of reproducibility tests with 22 flux measurement data sets from ten municipal solid waste landfills in the Republic of Korea were compared one another. The bilinear model and natural neighbor model among the deterministic models showed stable results in all cases. The surface methane emissions estimated from arithmetic or geometric mean resulted in significant under- or overestimation compared to spatial interpolation methods in all data sets. As a result of this study, minimal number of flux measurement points could be determined for target error levels. Innovative flux chamber network design with proper measurement points will improve the accuracy of methane emission estimate from solid waste landfills.

Modeling vaccination decision making process in a finite population

Vaccination is considered as one of the most crucial methods in controlling the spread of infectious diseases. However, it is difficult to predict the expected vaccine coverage level because it depends on human behaviors. We consider deterministic and stochastic models to simulate how individuals choose strategies in the scenario of vaccination. In an infinite population, a system of replicator equations is formulated and the expected level is calculated. Decision making processes in both an unstructured finite population and a structured finite population are discussed. Expected vaccine coverage levels are calculated and analyzed. In a structured finite population, passive decision making process and initiative decision making process are defined. It is also analytically and numerically proved that the passive decision making process can predict a higher vaccine coverage level than the process of initiative decision making.

Stochasticity and robustness analysis of microRNA-mediated ERK signaling network

MicroRNAs (miRNAs) play a critical role in regulating the signaling network such as the extracellular signal regulated kinase (ERK) pathway. However, the mechanisms of miRNA-mediated posttranscriptional regulations with regard to their impacts on signaling require further investigation from a systematic level. Therefore, we develop a mathematical model by analyzing the precise dynamic mechanisms with a bevy of miRNAs involved in the Ras/Raf/MEK/ERK pathway. A systems-based analysis approach is introduced into this model and the dynamics have been implemented deterministically and stochastically. Our analysis reveals that miRNAs are key participants regulating the gene expression of ERK network, and the cooperative actions of miRNAs are important in keeping the normal biological characteristics and amplification effects of the system. Meanwhile, the appearance of system disorder in the absence of miRNAs suggests that miRNAs may play a role in the pathological processes, such as tumor and inflammation. The sensitivity analysis and the kinetic parameter perturbation show that the binding of receptor (EGFR) and adaptor protein (Shc, Grb2 and Sos) under normal physiological conditions is crucial for the robustness of the whole pathway. In addition, the stochastic dynamic patterns are in a good agreement with the deterministic results, further demonstrating that the variability of the system due to the presence of some stochastic noise is low. All these will be helpful for a deeper understanding of the dynamic mechanism of miRNA-mediated ERK signal network, which might present a rich area of future research with the relevant regulatory roles of miRNAs in cell signaling pathway.

Be-CoDiS: A Mathematical Model to Predict the Risk of Human Diseases Spread Between Countries--Validation and Application to the 2014-2015 Ebola Virus Disease Epidemic

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the UK, the USA and Spain. Regarding the emergency of this situation, there is a need for the development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial-temporal model, called Between-Countries Disease Spread (Be-CoDiS), to study the evolution of human diseases within and between countries. The main interesting characteristics of Be-CoDiS are the consideration of the movement of people between countries, the control measure effects and the use of time-dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model and explain how its parameters and inputs are obtained. Then, in order to validate our approach, we consider two numerical experiments regarding the 2014-2015 Ebola epidemic. The first one studies the ability of the model in predicting the EVD evolution between countries starting from the index cases in Guinea in December 2013. The second one consists of forecasting the evolution of the epidemic by using some recent data. The results obtained with Be-CoDiS are compared to real data and other model outputs found in the literature. Finally, a brief parameter sensitivity analysis is done. A free MATLAB version of Be-CoDiS is available at: http://www.mat.ucm.es/momat/software.htm.

Nine challenges for deterministic epidemic models

Deterministic models have a long history of being applied to the study of infectious disease epidemiology. We highlight and discuss nine challenges in this area. The first two concern the endemic equilibrium and its stability. We indicate the need for models that describe multi-strain infections, infections with time-varying infectivity, and those where super infection is possible. We then consider the need for advances in spatial epidemic models, and draw attention to the lack of models that explore the relationship between communicable and non-communicable diseases. The final two challenges concern the uses and limitations of deterministic models as approximations to stochastic systems.