A Framework for Network-Based Epidemiological Modeling of Tuberculosis Dynamics Using Synthetic Datasets

Agent-based modelling of Mycobacterium tuberculosis transmission: a systematic review

BACKGROUND

Traditional epidemiological models tend to oversimplify the transmission dynamics of Mycobacterium tuberculosis (M.tb) to replicate observed tuberculosis (TB) epidemic patterns. This has led to growing interest in advanced methodologies like agent-based modelling (ABM), which can more accurately represent the complex heterogeneity of TB transmission.

OBJECTIVES

To better understand the use of agent-based models (ABMs) in this context, we conducted a systematic review with two main objectives: (1) to examine how ABMs have been employed to model the intricate heterogeneity of M.tb transmission, and (2) to identify the challenges and opportunities associated with implementing ABMs for M.tb.

SEARCH METHODS

We conducted a systematic search following PRISMA guidelines across four databases (MEDLINE, EMBASE, Global Health, and Scopus), limiting our review to peer-reviewed articles published in English up to December 2022. Data were extracted by two investigators using a standardized extraction tool. Prospero registration: CRD42022380580.

SELECTION CRITERIA

Our review included peer-reviewed articles in English that implement agent-based, individual-based, or microsimulation models of M.tb transmission. Models focusing solely on in-vitro or within-host dynamics were excluded. Data extraction targeted the methodological, epidemiological, and computational characteristics of ABMs used for TB transmission. A risk of bias assessment was not conducted as the review synthesized modelling studies without pooling epidemiological data.

RESULTS

Our search initially identified 5,077 studies, from which we ultimately included 26 in our final review after exclusions. These studies varied in population settings, time horizons, and model complexity. While many incorporated population heterogeneity and household structures, some lacked essential features like spatial structures or economic evaluations. Only eight studies provided publicly accessible code, highlighting the need for improved transparency.

AUTHORS' CONCLUSIONS

ABMs are a versatile approach for representing complex disease dynamics, particularly in cases like TB, where they address heterogeneous mixing and household transmission often overlooked by traditional models. However, their advanced capabilities come with challenges, including those arising from their stochastic nature, such as parameter tuning and high computational expense. To improve transparency and reproducibility, open-source code sharing, and standardised reporting are recommended to enhance ABM reliability in studying epidemiologically complex diseases like TB.

A social network analysis model approach to understand tuberculosis transmission in remote rural Madagascar

BACKGROUND

Quality surveillance data used to build tuberculosis (TB) transmission models are frequently unavailable and may overlook community intrinsic dynamics that impact TB transmission. Social network analysis (SNA) generates data on hyperlocal social-demographic structures that contribute to disease transmission.

METHODS

We collected social contact data in five villages and built SNA-informed village-specific stochastic TB transmission models in remote Madagascar. A name-generator approach was used to elicit individual contact networks. Recruitment included confirmed TB patients, followed by snowball sampling of named contacts. Egocentric network data were aggregated into village-level networks. Network- and individual-level characteristics determining contact formation and structure were identified by fitting an exponential random graph model (ERGM), which formed the basis of the contact structure and model dynamics. Models were calibrated and used to evaluate WHO-recommended interventions and community resiliency to foreign TB introduction.

RESULTS

Inter- and intra-village SNA showed variable degrees of interconnectivity, with transitivity (individual clustering) values of 0.16, 0.29, and 0.43. Active case finding and treatment yielded 67%-79% reduction in active TB disease prevalence and a 75% reduction in TB mortality in all village networks. Following hypothetical TB elimination and without specific interventions, networks A and B showed resilience to both active and latent TB reintroduction, while Network C, the village network with the highest transitivity, lacked resiliency to reintroduction and generated a TB prevalence of 2% and a TB mortality rate of 7.3% after introduction of one new contagious infection post hypothetical elimination.

CONCLUSION

In remote Madagascar, SNA-informed models suggest that WHO-recommended interventions reduce TB disease (active TB) prevalence and mortality while TB infection (latent TB) burden remains high. Communities' resiliency to TB introduction decreases as their interconnectivity increases. "Top down" population level TB models would most likely miss this difference between small communities. SNA bridges large-scale population-based and hyper focused community-level TB modeling.

A synthesized model of tuberculosis transmission featuring treatment abandonment

In this paper, we propose and justify a synthesized version of the tuberculosis transmission model featuring treatment abandonment. In contrast to other models that account for the treatment abandonment, our model has only four state variables or classes (susceptible, latent, infectious, and treated), while people abandoning treatment are not gathered into an additional class. The proposed model retains the core properties that are highly desirable in epidemiological modeling. Namely, the disease transmission dynamics is characterized by the basic reproduction number $ \mathscr{R}_0 $, a threshold value that determines the number of possible steady states and their stability properties. It is shown that the disease-free equilibrium is globally asymptotically stable (GAS) only if $ \mathscr{R}_0 < 1 $, while a strictly positive endemic equilibrium exists and is GAS only if $ \mathscr{R}_0 > 1. $ Analysis of the dependence of $ \mathscr{R}_0 $ on the treatment abandonment rate shows that a reduction of the treatment abandonment rate has a positive effect on the disease incidence and results in avoiding disease-related fatalities.

Transmission Dynamics of Tuberculosis with Age-specific Disease Progression

Demographic structure and latent phenomenon are two essential factors determining the rate of tuberculosis transmission. However, only a few mathematical models considered age structure coupling with disease stages of infectious individuals. This paper develops a system of delay partial differential equations to model tuberculosis transmission in a heterogeneous population. The system considers demographic structure coupling with the continuous development of disease stage, which is crucial for studying how aging affects tuberculosis dynamics and disease progression. Here, we determine the basic reproduction number, and several numerical simulations are used to investigate the influence of various progression rates on tuberculosis dynamics. Our results support that the aging effect on the disease progression rate contributes to tuberculosis permanence.

Evaluating Strategies For Tuberculosis to Achieve the Goals of WHO in China: A Seasonal Age-Structured Model Study

Although great progress has been made in the prevention and mitigation of TB in the past 20 years, China is still the third largest contributor to the global burden of new TB cases, accounting for 833,000 new cases in 2019. Improved mitigation strategies, such as vaccines, diagnostics, and treatment, are needed to meet goals of WHO. Given the huge variability in the prevalence of TB across age-groups in China, the vaccination, diagnostic techniques, and treatment for different age-groups may have different effects. Moreover, the statistics data of TB cases show significant seasonal fluctuations in China. In view of the above facts, we propose a non-autonomous differential equation model with age structure and seasonal transmission rate. We derive the basic reproduction number, [Formula: see text], and prove that the unique disease-free periodic solution, [Formula: see text] is globally asymptotically stable when [Formula: see text], while the disease is uniformly persistent and at least one positive periodic solution exists when [Formula: see text]. We estimate that the basic reproduction number [Formula: see text] ([Formula: see text]), which means that TB is uniformly persistent. Our results demonstrate that vaccinating susceptible individuals whose ages are over 65 and between 20 and 24 is much more effective in reducing the prevalence of TB, and each of the improved vaccination strategy, diagnostic strategy, and treatment strategy leads to substantial reductions in the prevalence of TB per 100,000 individuals compared with current approaches, and the combination of the three strategies is more effective. Scenario A (i.e., coverage rate [Formula: see text], diagnosis rate [Formula: see text], relapse rate [Formula: see text]) is the best and can reduce the prevalence of TB per 100,000 individuals by [Formula: see text] and [Formula: see text] in 2035 and 2050, respectively. Although the improved strategies will significantly reduce the incidence rate of TB, it is challenging to achieve the goal of WHO in 2050. Our findings can provide guidance for public health authorities in projecting effective mitigation strategies of TB.

Structural identifiability analysis of age-structured PDE epidemic models

Computational and mathematical models rely heavily on estimated parameter values for model development. Identifiability analysis determines how well the parameters of a model can be estimated from experimental data. Identifiability analysis is crucial for interpreting and determining confidence in model parameter values and to provide biologically relevant predictions. Structural identifiability analysis, in which one assumes data to be noiseless and arbitrarily fine-grained, has been extensively studied in the context of ordinary differential equation (ODE) models, but has not yet been widely explored for age-structured partial differential equation (PDE) models. These models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. In this work, we establish a pipeline for structural identifiability analysis of age-structured PDE models using a differential algebra framework and derive identifiability results for specific age-structured models. We use epidemic models to demonstrate this framework because of their wide-spread use in many different diseases and for the corresponding parallel work previously done for ODEs. In our application of the identifiability analysis pipeline, we focus on a Susceptible-Exposed-Infected model for which we compare identifiability results for a PDE and corresponding ODE system and explore effects of age-dependent parameters on identifiability. We also show how practical identifiability analysis can be applied in this example.

Predicting the second wave of COVID-19 in Washtenaw County, MI

The COVID-19 pandemic has highlighted the patchwork nature of disease epidemics, with infection spread dynamics varying wildly across countries and across states within the US. To explore this issue, we study and predict the spread of COVID-19 in Washtenaw County, MI, which is home to University of Michigan and Eastern Michigan University, and in close proximity to Detroit, MI, a major epicenter of the epidemic in Michigan. We apply a discrete and stochastic network-based modeling framework allowing us to track every individual in the county. In this framework, we construct contact networks based on synthetic population datasets specific for Washtenaw County that are derived from US Census datasets. We assign individuals to households, workplaces, schools, and group quarters (such as prisons or long term care facilities). In addition, we assign casual contacts to each individual at random. Using this framework, we explicitly simulate Michigan-specific government-mandated workplace and school closures as well as social distancing measures. We perform sensitivity analyses to identify key model parameters and mechanisms contributing to the observed disease burden in the three months following the first observed cases of COVID-19 in Michigan. We then consider several scenarios for relaxing restrictions and reopening workplaces to predict what actions would be most prudent. In particular, we consider the effects of 1) different timings for reopening, and 2) different levels of workplace vs. casual contact re-engagement. We find that delaying reopening does not reduce the magnitude of the second peak of cases, but only delays it. Reducing levels of casual contact, on the other hand, both delays and lowers the second peak. Through simulations and sensitivity analyses, we explore mechanisms driving the magnitude and timing of a second wave of infections upon re-opening. We find that the most significant factors are workplace and casual contacts and protective measures taken by infected individuals who have sought care. This model can be adapted to other US counties using synthetic population databases and data specific to those regions.

Predicting the second wave of COVID-19 in Washtenaw County, MI

Marissa Renardy and Denise Kirschner University of Michigan Medical School The COVID-19 pandemic has highlighted the patchwork nature of disease epidemics, with infection spread dynamics varying wildly across countries and across states within the US. These heteroge- neous patterns are also observed within individual states, with patches of concentrated outbreaks. Data is being generated daily at all of these spatial scales, and answers to questions regarded re- opening strategies are desperately needed. Mathematical modeling is useful in exactly these cases, and using modeling at a county scale may be valuable to further predict disease dynamics for the purposes of public health interventions. To explore this issue, we study and predict the spread of COVID-19 in Washtenaw County, MI, the home to University of Michigan, Eastern Michigan University, and Google, as well as serving as a sister city to Detroit, MI where there has been a serious outbreak. Here, we apply a discrete and stochastic network-based modeling framework allowing us to track every individual in the county. In this framework, we construct contact net- works based on synthetic population datasets specific for Washtenaw County that are derived from US Census datasets. We assign individuals to households, workplaces, schools, and group quarters (such as prisons). In addition, we assign casual contacts to each individual at random. Using this framework, we explicitly simulate Michigan-specific government-mandated workplace and school closures as well as social distancing measures. We also perform sensitivity analyses to identify key model parameters and mechanisms contributing to the observed disease burden in the three months following the first observed cases on COVID-19 in Michigan. We then consider several scenarios for relaxing restrictions and reopening workplaces to predict what actions would be most prudent. In particular, we consider the effects of 1) different timings for reopening, and 2) different levels of workplace vs. casual contact re-engagement. Through simulations and sensitivity analyses, we explore mechanisms driving magnitude and timing of a second wave of infections upon re-opening. This model can be adapted to other US counties using synthetic population databases and data specific to those regions.