Comparison of stochastic and deterministic frameworks in dengue modelling

Compartmental modeling for pandemic data analysis: The gap between statistics and models

A scrutiny analysis of the COVID-19 data is required to get insights into effective strategies for pandemic control. However, there is a gap between official data and methods used to assess the effectiveness of the potential measures, which was partly addressed in an editorial-letter-type discussion on the impact of the COVID-19 passport in Lithuania. The therein-applied descriptive statistics method provides only limited evidence, while detailed analysis requires more sensitive and reliable methods. In this regard, this paper advocates a maximum likelihood compartmental modeling approach, which provides the flexibility to raise various hypotheses about infection, recovery, and mortality dynamics and to find the most likely answers given the data. Our paper is based on COVID-19 deaths, which are more reliable and essential than infection cases. It should also be noted that officially collected data are unsuitable for in-depth analyses, including compartmental modeling, as they do not capture important information. Overall, this paper does not aim to solve the underlying problems completely but rather stimulate a discussion.

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.

Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties

Compartmental models are an important quantitative tool in epidemiology, enabling us to forecast the course of a communicable disease. However, the model parameters, such as the infectivity rate of the disease, are riddled with uncertainties, which has motivated the development and use of stochastic compartmental models. Here, we first show that a common stochastic model, which treats the uncertainties as white noise, is fundamentally flawed since it erroneously implies that greater parameter uncertainties will lead to the eradication of the disease. Then, we present a principled modelling of the uncertainties based on reasonable assumptions on the contacts of each individual. Using the central limit theorem and Doob’s theorem on Gaussian Markov processes, we prove that the correlated Ornstein–Uhlenbeck (OU) process is the appropriate tool for modelling uncertainties in the infectivity rate. We demonstrate our results using a compartmental model of the COVID-19 pandemic and the available US data from the Johns Hopkins University COVID-19 database. In particular, we show that the white noise stochastic model systematically underestimates the severity of the Omicron variant of COVID-19, whereas the OU model correctly forecasts the course of this variant. Moreover, using an SIS model of sexually transmitted disease, we derive an exact closed-form solution for the final distribution of infected individuals. This analytical result shows that the white noise model underestimates the severity of the pandemic because of unrealistic noise-induced transitions. Our results strongly support the need for temporal correlations in modelling of uncertainties in compartmental models of infectious disease.

Mathematical models for dengue fever epidemiology: A 10-year systematic review

Mathematical models have a long history in epidemiological research, and as the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. Mathematical models describing dengue fever epidemiological dynamics are found back from 1970. Dengue fever is a viral mosquito-borne infection caused by four antigenically related but distinct serotypes (DENV-1 to DENV-4). With 2.5 billion people at risk of acquiring the infection, it is a major international public health concern. Although most of the cases are asymptomatic or mild, the disease immunological response is complex, with severe disease linked to the antibody-dependent enhancement (ADE) - a disease augmentation phenomenon where pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection. Here, we present a 10-year systematic review on mathematical models for dengue fever epidemiology. Specifically, we review multi-strain frameworks describing host-to-host and vector-host transmission models and within-host models describing viral replication and the respective immune response. Following a detailed literature search in standard scientific databases, different mathematical models in terms of their scope, analytical approach and structural form, including model validation and parameter estimation using empirical data, are described and analyzed. Aiming to identify a consensus on infectious diseases modeling aspects that can contribute to public health authorities for disease control, we revise the current understanding of epidemiological and immunological factors influencing the transmission dynamics of dengue. This review provide insights on general features to be considered to model aspects of real-world public health problems, such as the current epidemiological scenario we are living in.

Dengue infection modeling and its optimal control analysis in East Java, Indonesia

In this study, we present a mathematical model of dengue fever transmission with hospitalization to describe the dynamics of the infection. We estimated the basic reproduction number for the infected cases in East Java Province for the year 2018 is R0≈1.1138. The parameters of the dengue model are estimated by using the confirmed notified cases of East Java province, Indonesia for the year 2018. We formulated the model for dengue with hospitalization and present its dynamics in details. Initially, we present the basic mathematical results and then show briefly the stability results for the model. Further, we formulate an optimal control problem with control functions and obtain the optimal control characterization. The optimal control problem is solved numerically and the results comprised of controls system for different strategies. The controls such as prevention and insecticide could use the best role in the disease eradication from the community. Our results suggest that the prevention of humans from the mosquitoes and the insecticide spray on mosquitoes can significantly reduce the infection of dengue fever and may reduce further spread of infection in the community.

Multi-cluster and environmental dependant vector born disease models

Vector-born disease models are extensively used for surveillance and control processes. The most simple and generally use model (SEIR-SEI model) cannot explain a variety of phenomena involved in these diseases spread and development. In order to obtain a wider insight of the vector-born disease models (and the dynamics involved in them), this work focuses into analyse the classical model, a modified versions of it, and 8 their parameters. The modified version includes host mobility, 9 environmental, re-susceptibility, and mosquito life cycle considerations. As results it is observed that there are a limiting number of parameters that play the most important roles in the dynamics (those related to mortality rates, recovery rate from infectious, and pathogen transmission probabilities). Therefore, parameters determination should focus primarily into estimate these values. Stronger effects of the environmental variables are observed and expected by using different parameters and/or the use of multiple environmental variable at the same time.

A Mapping Review on Urban Landscape Factors of Dengue Retrieved from Earth Observation Data, GIS Techniques, and Survey Questionnaires

To date, there is no effective treatment to cure dengue fever, a mosquito-borne disease which has a major impact on human populations in tropical and sub-tropical regions. Although the characteristics of dengue infection are well known, factors associated with landscape are highly scale dependent in time and space, and therefore difficult to monitor. We propose here a mapping review based on 78 articles that study the relationships between landscape factors and urban dengue cases considering household, neighborhood and administrative levels. Landscape factors were retrieved from survey questionnaires, Geographic Information Systems (GIS), and remote sensing (RS) techniques. We structured these into groups composed of land cover, land use, and housing type and characteristics, as well as subgroups referring to construction material, urban typology, and infrastructure level. We mapped the co-occurrence networks associated with these factors, and analyzed their relevance according to a three-valued interpretation (positive, negative, non significant). From a methodological perspective, coupling RS and GIS techniques with field surveys including entomological observations should be systematically considered, as none digital land use or land cover variables appears to be an univocal determinant of dengue occurrences. Remote sensing urban mapping is however of interest to provide a geographical frame to distribute human population and movement in relation to their activities in the city, and as spatialized input variables for epidemiological and entomological models.