Mathematical Modeling of "Chronic" Infectious Diseases: Unpacking the Black Box

Variance-based sensitivity analysis of tuberculosis transmission models

Mathematical models are widely used to provide evidence to inform policies for tuberculosis (TB) control. These models contain many sources of input uncertainty including the choice of model structure, parameter values and input data. Quantifying the role of these different sources of input uncertainty on the model outputs is important for understanding model dynamics and improving evidence for policy making. In this paper, we applied the Sobol sensitivity analysis method to a TB transmission model used to simulate the effects of a hypothetical population-wide screening strategy. We demonstrated how the method can be used to quantify the importance of both model parameters and model structure and how the analysis can be conducted on groups of inputs. Uncertainty in the model outputs was dominated by uncertainty in the intervention parameters. The important inputs were context dependent, depending on the setting, time horizon and outcome measure considered. In particular, the choice of model structure had an increasing effect on output uncertainty in high TB incidence settings. Grouping inputs identified the same influential inputs. Wider use of the Sobol method could inform ongoing development of infectious disease models and improve the use of modelling evidence in decision making.

Tuberculosis (TB) Aftermath: study protocol for a hybrid type I effectiveness-implementation non-inferiority randomized trial in India comparing two active case finding (ACF) strategies among individuals treated for TB and their household contacts

BACKGROUND

Approximately 7% of all reported tuberculosis (TB) cases each year are recurrent, occurring among people who have had TB in the recent or distant past. TB recurrence is particularly common in India, which has the largest TB burden worldwide. Although patients recently treated for TB are at high risk of developing TB again, evidence around effective active case finding (ACF) strategies in this population is scarce. We will conduct a hybrid type I effectiveness-implementation non-inferiority randomized trial to compare the effectiveness, cost-effectiveness, and feasibility of two ACF strategies among individuals who have completed TB treatment and their household contacts (HHCs).

METHODS

We will enroll 1076 adults (≥ 18 years) who have completed TB treatment at a public TB unit (TU) in Pune, India, along with their HHCs (averaging two per patient, n = 2152). Participants will undergo symptom-based ACF by existing healthcare workers (HCWs) at 6-month intervals and will be randomized to either home-based ACF (HACF) or telephonic ACF (TACF). Symptomatic participants will undergo microbiologic testing through the program. Asymptomatic HHCs will be referred for TB preventive treatment (TPT) per national guidelines. The primary outcome is rate per 100 person-years of people diagnosed with new or recurrent TB by study arm, within 12 months following treatment completion. The secondary outcome is proportion of HHCs < 6 years, by study arm, initiated on TPT after ruling out TB disease. Study staff will collect socio-demographic and clinical data to identify risk factors for TB recurrence and will measure post-TB lung impairment. In both arms, an 18-month "mop-up" visit will be conducted to ascertain outcomes. We will use the RE-AIM framework to characterize implementation processes and explore acceptability through in-depth interviews with index patients, HHCs and HCWs (n = 100). Cost-effectiveness will be assessed by calculating the incremental cost per TB case detected within 12 months and projected for disability-adjusted life years averted based on modeled estimates of morbidity, mortality, and time with infectious TB.

DISCUSSION

This novel trial will guide India's scale-up of post-treatment ACF and provide an evidence base for designing strategies to detect recurrent and new TB in other high burden settings.

TRIAL REGISTRATION

NCT04333485 , registered April 3, 2020. CTRI/2020/05/025059 [Clinical Trials Registry of India], registered May 6 2020.

Global research activity on mathematical modeling of transmission and control of 23 selected infectious disease outbreak

BACKGROUND

Mathematical analysis and modeling allow policymakers to understand and predict the dynamics of an infectious disease under several different scenarios. The current study aimed to analyze global research activity on mathematical modeling of transmission and control of several infectious diseases with a known history of serious outbreaks.

METHODS

Relevant publications were retrieved using a comprehensive validated search query. The database used was SciVerse Scopus. Indicators related to evolution, growth of publications, infectious diseases encountered, key players, citations, and international research collaboration were presented.

RESULTS

The search strategy found 5606. The growth of publications started in 1967 and showed a sharp rise in 2020 and 2021. The retrieved articles received relatively high citations (h-index = 158). Despite being multidisciplinary, Plos One journal made the highest contribution to the field. The main findings of the study are summarized as follows: (a) COVID-19 had a strong impact on the number of publications in the field, specifically during the years 2020 and 2021; (b) research in the field was published in a wide range of journals, mainly those in the field of infectious diseases and mathematical sciences; (c) research in the field was mainly published by scholars in the United States and the United Kingdom; (d) international research collaboration between active countries and less developed countries was poor; (e) research activity relied on research groups with a large number of researchers per group indicative of good author-author collaboration; (f) HIV/AIDS, coronavirus disease, influenza, and malaria were the most frequently researched diseases; (g) recently published articles on COVID-19 received the highest number of citations; and (h) researchers in the Eastern Mediterranian and South-East Asian regions made the least contribution to the retrieved articles.

CONCLUSION

Mathematical modeling is gaining popularity as a tool for understanding the dynamics of infectious diseases. The application of mathematical modeling on new emerging infectious disease outbreaks is a priority. Research collaboration with less developed countries in the field of mathematical epidemiology is needed and should be prioritized and funded.

Potential Effects of the Coronavirus Disease 2019 (COVID-19) Pandemic on Human Immunodeficiency Virus (HIV) Transmission: A Modeling Study in 32 US Cities

BACKGROUND

The degree to which the 2019 novel coronavirus disease (COVID-19) pandemic will affect the US human immunodeficiency virus (HIV) epidemic is unclear.

METHODS

We used the Johns Hopkins Epidemiologic and Economic Model to project HIV infections from 2020 to 2025 in 32 US metropolitan statistical areas (MSAs). We sampled a range of effects of the pandemic on sexual transmission (0-50% reduction), viral suppression among people with HIV (0-40% reduction), HIV testing (0-50% reduction), and pre-exposure prophylaxis use (0-30% reduction), and indexed reductions over time to Google Community Mobility Reports.

RESULTS

Simulations projected reported diagnoses would drop in 2020 and rebound in 2021 or 2022, regardless of underlying incidence. If sexual transmission normalized by July 2021 and HIV care normalized by January 2022, we projected 1161 (1%) more infections from 2020 to 2025 across all 32 cities than if COVID-19 had not occurred. Among "optimistic" simulations in which sexual transmission was sharply reduced and viral suppression was maintained we projected 8% lower incidence (95% credible interval: 14% lower to no change). Among "pessimistic" simulations where sexual transmission was largely unchanged but viral suppression fell, we projected 11% higher incidence (1-21% higher). MSA-specific projections are available at www.jheem.org?covid.

CONCLUSIONS

The effects of COVID-19 on HIV transmission remain uncertain and differ between cities. Reported diagnoses of HIV in 2020-2021 are likely to correlate poorly with underlying incidence. Minimizing disruptions to HIV care is critical to mitigating negative effects of the COVID-19 pandemic on HIV transmission.

What Will It Take to End HIV in the United States? : A Comprehensive, Local-Level Modeling Study

BACKGROUND

The Ending the HIV Epidemic (EHE) initiative aims to reduce incident HIV infections by 90% over a span of 10 years. The intensity of interventions needed to achieve this for local epidemics is unclear.

OBJECTIVE

To estimate the effect of HIV interventions at the city level.

DESIGN

A compartmental model of city-level HIV transmission stratified by age, race, sex, and HIV risk factor was developed and calibrated.

SETTING

32 priority metropolitan statistical areas (MSAs).

PATIENTS

Simulated populations in each MSA.

INTERVENTION

Combinations of HIV testing and preexposure prophylaxis (PrEP) coverage among those at risk for HIV, plus viral suppression in persons with diagnosed HIV infection.

MEASUREMENTS

The primary outcome was the projected reduction in incident cases from 2020 to 2030.

RESULTS

Absent intervention, HIV incidence was projected to decrease by 19% across all 32 MSAs. Modest increases in testing (1.25-fold per year), PrEP coverage (5 percentage points), and viral suppression (10 percentage points) across the population could achieve reductions of 34% to 67% by 2030. Twenty-five percent PrEP coverage, testing twice a year on average, and 90% viral suppression among young Black and Hispanic men who have sex with men (MSM) achieved similar reductions (13% to 68%). Including all MSM and persons who inject drugs could reduce incidence by 48% to 90%. Thirteen of 32 MSAs could achieve greater than 90% reductions in HIV incidence with large-scale interventions that include heterosexuals. A web application with location-specific results is publicly available (www.jheem.org).

LIMITATION

The COVID-19 pandemic was not represented.

CONCLUSION

Large reductions in HIV incidence are achievable with substantial investment, but the EHE goals will be difficult to achieve in most locations. An interactive model that can help policymakers maximize the effect in their local environments is presented.

PRIMARY FUNDING SOURCE

National Institutes of Health.

The predicted impact of tuberculosis preventive therapy: the importance of disease progression assumptions

BACKGROUND

Following infection with Mycobacterium tuberculosis (M.tb), individuals may rapidly develop tuberculosis (TB) disease or enter a "latent" infection state with a low risk of progression to disease. Mathematical models use a variety of structures and parameterisations to represent this process. The effect of these different assumptions on the predicted impact of TB interventions has not been assessed.

METHODS

We explored how the assumptions made about progression from infection to disease affect the predicted impact of TB preventive therapy. We compared the predictions using three commonly used model structures, and parameters derived from two different data sources.

RESULTS

The predicted impact of preventive therapy depended on both the model structure and parameterisation. At a baseline annual TB incidence of 500/100,000, there was a greater than 2.5-fold difference in the predicted reduction in incidence due to preventive therapy (ranging from 6 to 16%), and the number needed to treat to avert one TB case varied between 67 and 157. The relative importance of structure and parameters depended on baseline TB incidence and assumptions about the efficacy of preventive therapy, with the choice of structure becoming more important at higher incidence.

CONCLUSIONS

The assumptions use to represent progression to disease in models are likely to influence the predicted impact of preventive therapy and other TB interventions. Modelling estimates of TB preventive therapy should consider routinely incorporating structural uncertainty, particularly in higher burden settings. Not doing so may lead to inaccurate and over confident conclusions, and sub-optimal evidence for decision making.

Calibration of individual-based models to epidemiological data: A systematic review

Individual-based models (IBMs) informing public health policy should be calibrated to data and provide estimates of uncertainty. Two main components of model-calibration methods are the parameter-search strategy and the goodness-of-fit (GOF) measure; many options exist for each of these. This review provides an overview of calibration methods used in IBMs modelling infectious disease spread. We identified articles on PubMed employing simulation-based methods to calibrate IBMs informing public health policy in HIV, tuberculosis, and malaria epidemiology published between 1 January 2013 and 31 December 2018. Articles were included if models stored individual-specific information, and calibration involved comparing model output to population-level targets. We extracted information on parameter-search strategies, GOF measures, and model validation. The PubMed search identified 653 candidate articles, of which 84 met the review criteria. Of the included articles, 40 (48%) combined a quantitative GOF measure with an algorithmic parameter-search strategy–either an optimisation algorithm (14/40) or a sampling algorithm (26/40). These 40 articles varied widely in their choices of parameter-search strategies and GOF measures. For the remaining 44 (52%) articles, the parameter-search strategy could either not be identified (32/44) or was described as an informal, non-reproducible method (12/44). Of these 44 articles, the majority (25/44) were unclear about the GOF measure used; of the rest, only five quantitatively evaluated GOF. Only a minority of the included articles, 14 (17%) provided a rationale for their choice of model-calibration method. Model validation was reported in 31 (37%) articles. Reporting on calibration methods is far from optimal in epidemiological modelling studies of HIV, malaria and TB transmission dynamics. The adoption of better documented, algorithmic calibration methods could improve both reproducibility and the quality of inference in model-based epidemiology. There is a need for research comparing the performance of calibration methods to inform decisions about the parameter-search strategies and GOF measures.

Calibration—that is, “fitting” the model to data—is a crucial part of using mathematical models to better forecast and control the population-level spread of infectious diseases. Evidence that the mathematical model is well-calibrated improves confidence that the model provides a realistic picture of the consequences of health policy decisions. To make informed decisions, Policymakers need information about uncertainty: i.e., what is the range of likely outcomes (rather than just a single prediction). Thus, modellers should also strive to provide accurate measurements of uncertainty, both for their model parameters and for their predictions. This systematic review provides an overview of the methods used to calibrate individual-based models (IBMs) of the spread of HIV, malaria, and tuberculosis. We found that less than half of the reviewed articles used reproducible, non-subjective calibration methods. For the remaining articles, the method could either not be identified or was described as an informal, non-reproducible method. Only one-third of the articles obtained estimates of parameter uncertainty. We conclude that the adoption of better-documented, algorithmic calibration methods could improve both reproducibility and the quality of inference in model-based epidemiology.

Projecting the impact of variable MDR-TB transmission efficiency on long-term epidemic trends in South Africa and Vietnam

Whether multidrug-resistant tuberculosis (MDR-TB) is less transmissible than drug-susceptible (DS-)TB on a population level is uncertain. Even in the absence of a genetic fitness cost, the transmission potential of individuals with MDR-TB may vary by infectiousness, frequency of contact, or duration of disease. We used a compartmental model to project the progression of MDR-TB epidemics in South Africa and Vietnam under alternative assumptions about the relative transmission efficiency of MDR-TB. Specifically, we considered three scenarios: consistently lower transmission efficiency for MDR-TB than for DS-TB; equal transmission efficiency; and an initial deficit in the transmission efficiency of MDR-TB that closes over time. We calibrated these scenarios with data from drug resistance surveys and projected epidemic trends to 2040. The incidence of MDR-TB was projected to expand in most scenarios, but the degree of expansion depended greatly on the future transmission efficiency of MDR-TB. For example, by 2040, we projected absolute MDR-TB incidence to account for 5% (IQR: 4–9%) of incident TB in South Africa and 14% (IQR: 9–26%) in Vietnam assuming consistently lower MDR-TB transmission efficiency, versus 15% (IQR: 8–27%)and 41% (IQR: 23–62%), respectively, assuming shrinking transmission efficiency deficits. Given future uncertainty, specific responses to halt MDR-TB transmission should be prioritized.

Investigation of house dust mite induced allergy using logistic regression in West Bengal, India

BACKGROUND

The diagnosis of house dust mite (HDM) allergy based on Skin prick test (SPT) is not accurate, especially in lower risk cases. Our aim is to develop and validate a predictive model to diagnose the HDM allergic symptoms (urticaria, allergic rhinitis, asthma).

METHODS

A forward-step logistic regression model was developed using a data set of 537 patients of West Bengal, India consisting of clinical variables (SPT based on 6 allergens of house dust and house dust mites, total IgE) and demographic characteristics (age, sex, house conditions). The output probability was estimated from the allergic symptoms shown by the patients. We finally prospectively validated a data set of 600 patients.

RESULTS

The gradual inclusion of the variables increased the correlation between observed and predicted probabilities (correlation coefficient (r2) = 0.97). The model development using group-1 showed an accuracy rate of 99%, sensitivity and specificity of 99.7% and 88.6% respectively and the area under the receiver operating characteristics (ROC) curve (AUC) of 99%. The corresponding numbers for the validation of our model with group-2 were 87%, 95.6% and 66% and 86% respectively. The model predicted the probability of symptoms better than SPTs in combination (accuracy rate 0.76-0.80), especially in lower risk cases (probability< 0.8) that are highly difficult to diagnose.

CONCLUSION

This is perhaps the first attempt to model the outcome of HDM allergy in terms of symptoms, which could open up an alternative but highly efficient way for accurate diagnosis of HDM allergy enhancing the efficiency of immunotherapy.

Improving the quality of modelling evidence used for tuberculosis policy evaluation

Mathematical modelling is commonly used to evaluate policy options for tuberculosis (TB) control in high-burden countries. Although major policy and funding decisions are made based on these analyses, there is concern about the variability of results produced using modelled policy analyses. We discuss new guidance for country-level TB policy modelling. The guidance was developed by the TB Modelling and Analysis Consortium in collaboration with the World Health Organization Global TB Programme, with input from a range of TB stakeholders (funders, modelling groups, country TB programme staff and subject matter experts). The guidance describes principles for country-level TB modelling, as well as good practices for operationalising the principles. The principles cover technical concerns such as model design, parameterisation and validation, as well as approaches for incorporating modelling into country-led policy making and budgeting. For modellers, this guidance suggests approaches to improve the quality and relevance of modelling undertaken to support country-level planning. For non-modellers, this guidance describes considerations for engaging modelling technical assistance, contributing to a modelling exercise and reviewing the results of modelled analyses. If routinely adopted, this guidance should improve the reliability, transparency and usefulness of modelling for country-level TB policy making. However, this guidance will not address all challenges facing modelling, and ongoing work is needed to improve the empirical evidence base for TB policy evaluation and develop stronger mechanisms for validating models. Increasing country ownership of the modelling process remains a challenge, requiring sustained engagement and capacity building.