Disease modeling for public health: added value, challenges, and institutional constraints

Evidence-based Decision Making: Infectious Disease Modeling Training for Policymakers in East Africa

Background

Mathematical modeling of infectious diseases is an important decision-making tool for outbreak control. However, in Africa, limited expertise reduces the use and impact of these tools on policy. Therefore, there is a need to build capacity in Africa for the use of mathematical modeling to inform policy. Here we describe our experience implementing a mathematical modeling training program for public health professionals in East Africa.

Methods

We used a deliverable-driven and learning-by-doing model to introduce trainees to the mathematical modeling of infectious diseases. The training comprised two two-week in-person sessions and a practicum where trainees received intensive mentorship. Trainees evaluated the content and structure of the course at the end of each week, and this feedback informed the strategy for subsequent weeks.

Findings

Out of 875 applications from 38 countries, we selected ten trainees from three countries - Rwanda (6), Kenya (2), and Uganda (2) - with guidance from an advisory committee. Nine trainees were based at government institutions and one at an academic organization. Participants gained skills in developing models to answer questions of interest and critically appraising modeling studies. At the end of the training, trainees prepared policy briefs summarizing their modeling study findings. These were presented at a dissemination event to policymakers, researchers, and program managers. All trainees indicated they would recommend the course to colleagues and rated the quality of the training with a median score of 9/10.

Conclusions

Mathematical modeling training programs for public health professionals in Africa can be an effective tool for research capacity building and policy support to mitigate infectious disease burden and forecast resources. Overall, the course was successful, owing to a combination of factors, including institutional support, trainees' commitment, intensive mentorship, a diverse trainee pool, and regular evaluations.

A competency framework on simulation modelling-supported decision-making for Master of Public Health graduates

BACKGROUND

Simulation models are increasingly important for supporting decision-making in public health. However, due to lack of training, many public health professionals remain unfamiliar with constructing simulation models and using their outputs for decision-making. This study contributes to filling this gap by developing a competency framework on simulation model-supported decision-making targeting Master of Public Health education.

METHODS

The study combined a literature review, a two-stage online Delphi survey and an online consensus workshop. A draft competency framework was developed based on 28 peer-reviewed publications. A two-stage online Delphi survey involving 15 experts was conducted to refine the framework. Finally, an online consensus workshop, including six experts, evaluated the competency framework and discussed its implementation.

RESULTS

The competency framework identified 20 competencies related to stakeholder engagement, problem definition, evidence identification, participatory system mapping, model creation and calibration and the interpretation and dissemination of model results. The expert evaluation recommended differentiating professional profiles and levels of expertise and synergizing with existing course contents to support its implementation.

CONCLUSIONS

The competency framework developed in this study is instrumental to including simulation model-supported decision-making in public health training. Future research is required to differentiate expertise levels and develop implementation strategies.

[Evolution and Application of Disease Control Priorities]

Disease control priority (DCP) is an important public health intervention strategy. Diseases that should be prioritized for prevention and control are first screened with a series of criteria, including the severity of the disease burden, the effectiveness of disease control technologies, the prevention and control capacity of the existing health system, etc. Then, the prevention and control technologies for these diseases undergo qualitative evaluation (eg, face-to-face interviews, expert consultation, workshops, etc) and quantitative evaluation (eg, cost-benefit analysis, multi-criteria decision analysis, etc). Finally, the public health initiatives that should be prioritized are identified. From the conception of the idea, to the formal proposition of the concept, to guidance for practice, DCP has gone through more than 70 years of development. Through DCP, significant contributions has been made to improving the efficiency of health care service systems and promoting the health of populations in developing countries. Herein, we systematically reviewed the background, development history, realization method, and practical applications of DCP, focusing on exploring the application potential of DCP in health governance and providing technical support and decision-making reference for the comprehensive promotion of the Healthy China Initiative.

Modelling outbreak response impact in human vaccine-preventable diseases: A systematic review of differences in practices between collaboration types before COVID-19

BACKGROUND

Outbreak response modelling often involves collaboration among academics, and experts from governmental and non-governmental organizations. We conducted a systematic review of modelling studies on human vaccine-preventable disease (VPD) outbreaks to identify patterns in modelling practices between two collaboration types. We complemented this with a mini comparison of foot-and-mouth disease (FMD), a veterinary disease that is controllable by vaccination.

METHODS

We searched three databases for modelling studies that assessed the impact of an outbreak response. We extracted data on author affiliation type (academic institution, governmental, and non-governmental organizations), location studied, and whether at least one author was affiliated to the studied location. We also extracted the outcomes and interventions studied, and model characteristics. Included studies were grouped into two collaboration types: purely academic (papers with only academic affiliations), and mixed (all other combinations) to help investigate differences in modelling patterns between collaboration types in the human disease literature and overall differences with FMD collaboration practices.

RESULTS

Human VPDs formed 227 of 252 included studies. Purely academic collaborations dominated the human disease studies (56%). Notably, mixed collaborations increased in the last seven years (2013-2019). Most studies had an author affiliated to an institution in the country studied (75.2%) but this was more likely among the mixed collaborations. Contrasted to the human VPDs, mixed collaborations dominated the FMD literature (56%). Furthermore, FMD studies more often had an author with an affiliation to the country studied (92%) and used complex model design, including stochasticity, and model parametrization and validation.

CONCLUSION

The increase in mixed collaboration studies over the past seven years could suggest an increase in the uptake of modelling for outbreak response decision-making. We encourage more mixed collaborations between academic and non-academic institutions and the involvement of locally affiliated authors to help ensure that the studies suit local contexts.

How Could Different Obesity Scenarios Alter the Burden of Type 2 Diabetes and Liver Disease in Saudi Arabia?

INTRODUCTION

Obesity is a major risk factor for type 2 diabetes (T2DM) and liver disease, and obesity-attributable liver disease is a common indication for liver transplant. Obesity prevalence in Saudi Arabia (SA) has increased in recent decades. SA has committed to the WHO "halt obesity" target to shift prevalence to 2010 levels by 2025. We estimated the future benefits of reducing obesity in SA on incidence and costs of T2DM and liver disease under two policy scenarios: (1) SA meets the "halt obesity" target; (2) population body mass index (BMI) is reduced by 1% annually from 2020 to 2040.

METHODS

We developed a dynamic microsimulation of working-age people (20-59 years) in SA between 2010 and 2040. Model inputs included population demographic, disease and healthcare cost data, and relative risks of diseases associated with obesity. In our two policy scenarios, we manipulated population BMI and compared predicted disease incidence and associated healthcare costs to a baseline "no change" scenario.

RESULTS

Adults <35 years are expected to meet the "halt obesity" target, but those ≥35 years are not. Obesity is set to decline for females, but to increase amongst males 35-59 years. If SA's working-age population achieved either scenario, >1.15 million combined cases of T2DM, liver disease, and liver cancer could be avoided by 2040. Healthcare cost savings for the "halt obesity" and 1% reduction scenarios are 46.7 and 32.8 billion USD, respectively.

CONCLUSION

SA's younger working-age population is set to meet the "halt obesity" target, but those aged 35-59 are off track. Even a modest annual 1% BMI reduction could result in substantial future health and economic benefits. Our findings strongly support universal initiatives to reduce population-level obesity, with targeted initiatives for working-age people ≥35 years of age.

The estimated dietary and health impact of implementing the recently approved 'high in' front-of-package nutrition symbol in Canada: a food substitution scenario modeling study

Background

Front-of-pack labeling (FOPL) has been identified as a cost-effective policy to promote healthy food environments and to help consumers make healthier food choices. Consumer surveys report that after implementation of mandatory 'high in' FOPL symbols between 30 and 70% of consumers choose or were willing to choose products with fewer 'high in' symbols. Health Canada has recently published FOPL regulations that will require prepackaged food and beverages that meet or exceed thresholds for sodium, total sugars, or saturated fat to display a 'high in' FOPL nutrition symbol.

Objectives

The aims were to estimate the potential (1) dietary impact of substituting foods with similar foods that would display at least one less 'high in' symbol, and (2) the number of diet-related noncommunicable disease (NCD) deaths that could be averted or delayed due to estimated dietary changes.

Methods

Baseline and counterfactual intakes of sodium, total sugars, saturated fats, and energy were estimated among Canadian adults (n = 11,992) using both available days of 24 h-recall data from the 2015 Canadian Community Health Survey-Nutrition (CCHS). Similar foods to those reported in CCHS that would display at least one less 'high in' symbol (n = 239) were identified using a Canadian branded food composition database. Based on current FOPL consumer research, identified foods were substituted for 30, 50, and 70% of randomly selected CCHS-Nutrition adult participants and for all adult participants. Potential health impacts were estimated using the Preventable Risk Integrated ModEl.

Results

Mean dietary reductions of between 73 and 259 mg/day of sodium, 2.0 and 6.9 g/day of total sugars, 0.2 and 0.5 g/day of saturated fats, and 14 and 46 kcal/day of energy were estimated. Between 2,148 (95% UI 1,913-2,386) and 7,047 (95% UI 6,249-7,886) of deaths due to diet-related NCDs, primarily from cardiovascular diseases (70%), could potentially be averted or delayed if Canadians choose products with fewer 'high in' symbols.

Conclusion

Results suggest that FOPL could significantly reduce sodium and total sugar intakes among Canadian adults, the consequences of which could avert or delay an important number of diet-related NCD deaths. These findings provide relevant data to support the importance of the impending FOPL regulations.

How Many Diet-Related Non-Communicable Disease Deaths Could Be Averted or Delayed If Canadians Reduced Their Consumption of Calories Derived from Free Sugars Intake? A Macrosimulation Modeling Study

Free sugars are a major source of calories in diets and contribute to the burden of many non-communicable diseases (NCDs). The World Health Organization (WHO) recommends reducing free sugars intake to less than 10% of total energy. This study aimed to estimate the number of diet-related NCD deaths which could be averted or delayed if Canadian adults were to reduce their calorie intake due to a systematic 20% reduction in the free sugars content in foods and beverages in Canada. We used the Preventable Risk Integrated ModEl (PRIME) to estimate the potential health impact. An estimated 6770 (95% UI 6184-7333) deaths due to diet-related NCDs could be averted or delayed, mostly from cardiovascular diseases (66.3%). This estimation would represent 7.5% of diet-related NCD deaths observed in 2019 in Canada. A 20% reduction in the free sugars content in foods and beverages would lead to a 3.2% reduction in calorie intake, yet an important number of diet-related NCD deaths could be averted or delayed through this strategy. Our findings can inform future policy decisions to support Canadians' free sugars intake reduction, such as proposing target levels for the free sugars content in key food categories.

Using compartmental models and Particle Swarm Optimization to assess Dengue basic reproduction number R 0 for the Republic of Panama in the 1999-2022 period

Nowadays, the ability to make data-driven decisions in public health is of utmost importance. To achieve this, it is necessary for modelers to comprehend the impact of models on the future state of healthcare systems. Compartmental models are a valuable tool for making informed epidemiological decisions, and the proper parameterization of these models is crucial for analyzing epidemiological events. This work evaluated the use of compartmental models in conjunction with Particle Swarm Optimization (PSO) to determine optimal solutions and understand the dynamics of Dengue epidemics. The focus was on calculating and evaluating the rate of case reproduction, R 0 , for the Republic of Panama. Three compartmental models were compared: Susceptible-Infected-Recovered (SIR), Susceptible-Exposed-Infected-Recovered (SEIR), and Susceptible-Infected-Recovered Human-Susceptible-Infected Vector (SIR Human-SI Vector, SIR-SI). The models were informed by demographic data and Dengue incidence in the Republic of Panama between 1999 and 2022, and the susceptible population was analyzed. The SIR, SEIR, and SIR-SI models successfully provided R 0 estimates ranging from 1.09 to 1.74. This study provides, to the best of our understanding, the first calculation of R 0 for Dengue outbreaks in the Republic of Panama.

Estimating the dietary and health impact of implementing front-of-pack nutrition labeling in Canada: A macrosimulation modeling study

Background

Front-of-pack labeling (FOPL) has been identified as a cost-effective policy to promote healthy diets. Health Canada has recently published FOPL regulations that will require food and beverages that meet or exceed set thresholds for sodium, sugars, or saturated fat to display a 'high in' symbol on the front of the package. Although a promising measure, its potential impact on dietary intakes and health have not yet been estimated in Canada.

Objective

This study aims to estimate (1) the potential dietary impact of implementing a mandatory FOPL among Canadian adults; and (2) the number of diet-related non-communicable disease (NCD) deaths that could be averted or delayed due to these estimated dietary changes.

Methods

Baseline and counterfactual usual intakes of sodium, total sugars, saturated fats, and calories were estimated among Canadian adults (n = 11,992) using both available days of 24 h recalls from the 2015 Canadian Community Health Survey-Nutrition. The National Cancer Institute method was used to estimate usual intakes, and adjusted for age, sex, misreporting status, weekend/weekday, and sequence of recall. Estimated counterfactual dietary intakes were modeled from reductions observed in experimental and observational studies that examined changes in sodium, sugars, saturated fat, and calorie content of food purchases in the presence of a 'high in' FOPL (four counterfactual scenarios). The Preventable Risk Integrated ModEl was used to estimate potential health impacts.

Results

Estimated mean dietary reductions were between 31 and 212 mg/day of sodium, 2.3 and 8.7 g/day of total sugars, 0.8 and 3.7 g/day of saturated fats, and 16 and 59 kcal/day of calories. Between 2,183 (95% UI 2,008-2,361) and 8,907 (95% UI 8,095-9,667) deaths due to diet-related NCDs, mostly from cardiovascular diseases (~70%), could potentially be averted or delayed by implementing a 'high in' FOPL in Canada. This estimation represents between 2.4 and 9.6% of the total number of diet-related NCD deaths in Canada.

Conclusion

Results suggest that implementing a FOPL could significantly reduce sodium, total sugar, and saturated fat intakes among Canadian adults and subsequently prevent or postpone a substantial number of diet-related NCD deaths in Canada. These results provide critical evidence to inform policy decisions related to implementing FOPL in Canada.

Estimating Canadian sodium intakes and the health impact of meeting national and WHO recommended sodium intake levels: A macrosimulation modelling study

BACKGROUND

Cardiovascular diseases (CVDs) are the second leading cause of total deaths in Canada. High blood pressure is the main metabolic risk factor for developing CVDs. It has been well established that excess consumption of sodium adversely affects blood pressure. Canadians' mean sodium intakes are well above recommended levels. Reducing dietary sodium intake through food reformulation has been identified as a cost-effective intervention, however, dietary sodium intake and the potential health impact of meeting recommended sodium intake levels due to food reformulation have not been determined in Canada.

OBJECTIVE

This study aimed to 1) obtain robust estimates of Canadians' usual sodium intakes, 2) model sodium intakes had foods been reformulated to align with Health Canada's sodium reduction targets, and 3) estimate the number of CVD deaths that could be averted or delayed if Canadian adults were to reduce their mean sodium intake to recommended levels under three scenarios: A) 2,300 mg/d-driven by a reduction of sodium levels in packaged foods to meet Health Canada targets (reformulation); B) 2,000 mg/d to meet the World Health Organization (WHO) recommendation; and C) 1,500 mg/d to meet the Adequate Intake recommendation.

METHODS

Foods in the University of Toronto's Food Label Information Program 2017, a Canadian branded food composition database, were linked to nationally representative food intake data from the 2015 Canadian Community Health Survey-Nutrition to estimate sodium intakes (and intakes had Health Canada's reformulation strategy been fully implemented). The Preventable Risk Integrated ModEl (PRIME) was used to estimate potential health impact.

RESULTS

Overall, mean sodium intake was 2758 mg/day, varying by age and sex group. Based on 'reformulation' scenario A, mean sodium intakes were reduced by 459 mg/day, to 2299 mg/day. Reducing Canadians' sodium intake to recommended levels under scenarios A, B and C could have averted or delayed 2,176 (95% UI 869-3,687), 3,252 (95% UI 1,380-5,321), and 5,296 (95% UI 2,190-8,311) deaths due to CVDs, respectively, mainly from ischaemic heart disease, stroke, and hypertensive disease. This represents 3.7%, 5.6%, and 9.1%, respectively, of the total number of CVDs deaths observed in Canada in 2019.

CONCLUSION

Results suggest that reducing sodium intake to recommended levels could prevent or postpone a substantial number of CVD deaths in Canada. Reduced sodium intakes could be achieved through reformulation of the Canadian food supply. However, it will require higher compliance from the food industry to achieve Health Canada's voluntary benchmark sodium reduction targets.

Estimation of timing of infection from longitudinal SARS-CoV-2 viral load data: mathematical modelling study

Background

Multiple waves of the COVID-19 epidemic have hit most countries by the end of 2021. Most of those waves are caused by emergence and importation of new variants. To prevent importation of new variants, combination of border control and contact tracing is essential. However, the timing of infection inferred by interview is influenced by recall bias and hinders the contact tracing process.

Methods

We propose a novel approach to infer the timing of infection, by employing a within-host model to capture viral load dynamics after the onset of symptoms. We applied this approach to ascertain secondary transmission which can trigger outbreaks. As a demonstration, the 12 initial reported cases in Singapore, which were considered as imported because of their recent travel history to Wuhan, were analyzed to assess whether they are truly imported.

Results

Our approach suggested that 6 cases were infected prior to the arrival in Singapore, whereas other 6 cases might have been secondary local infection. Three among the 6 potential secondary transmission cases revealed that they had contact history to previously confirmed cases.

Conclusions

Contact trace combined with our approach using viral load data could be the key to mitigate the risk of importation of new variants by identifying cases as early as possible and inferring the timing of infection with high accuracy.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-022-07646-2.

Leveraging mathematical models of disease dynamics and machine learning to improve development of novel malaria interventions

Background

Substantial research is underway to develop next-generation interventions that address current malaria control challenges. As there is limited testing in their early development, it is difficult to predefine intervention properties such as efficacy that achieve target health goals, and therefore challenging to prioritize selection of novel candidate interventions. Here, we present a quantitative approach to guide intervention development using mathematical models of malaria dynamics coupled with machine learning. Our analysis identifies requirements of efficacy, coverage, and duration of effect for five novel malaria interventions to achieve targeted reductions in malaria prevalence.

Methods

A mathematical model of malaria transmission dynamics is used to simulate deployment and predict potential impact of new malaria interventions by considering operational, health-system, population, and disease characteristics. Our method relies on consultation with product development stakeholders to define the putative space of novel intervention specifications. We couple the disease model with machine learning to search this multi-dimensional space and efficiently identify optimal intervention properties that achieve specified health goals.

Results

We apply our approach to five malaria interventions under development. Aiming for malaria prevalence reduction, we identify and quantify key determinants of intervention impact along with their minimal properties required to achieve the desired health goals. While coverage is generally identified as the largest driver of impact, higher efficacy, longer protection duration or multiple deployments per year are needed to increase prevalence reduction. We show that interventions on multiple parasite or vector targets, as well as combinations the new interventions with drug treatment, lead to significant burden reductions and lower efficacy or duration requirements.

Conclusions

Our approach uses disease dynamic models and machine learning to support decision-making and resource investment, facilitating development of new malaria interventions. By evaluating the intervention capabilities in relation to the targeted health goal, our analysis allows prioritization of interventions and of their specifications from an early stage in development, and subsequent investments to be channeled cost-effectively towards impact maximization. This study highlights the role of mathematical models to support intervention development. Although we focus on five malaria interventions, the analysis is generalizable to other new malaria interventions.

Graphical abstract

Supplementary Information

The online version contains supplementary material available at 10.1186/s40249-022-00981-1.

Mechanisms of biodiversity between Campylobacter sequence types in a flock of broiler–breeder chickens

Commercial poultry flocks frequently harbor the dangerous bacterial pathogen Campylobacter. As exclusion efforts frequently fail, there is interest in potential ecologically informed solutions. A long‐term study of Campylobacter sequence types was used to investigate the competitive framework of the Campylobacter metacommunity and understand how multiple sequence types simultaneously co‐occur in a flock of chickens. A combination of matrix and patch‐occupancy models was used to estimate parameters describing the competition, transmission, and mortality of each sequence type. It was found that Campylobacter sequence types form a strong hierarchical framework within a flock of chickens and occupied a broad spectrum of transmission–mortality trade‐offs. Upon further investigation of how biodiversity is thus maintained within the flock, it was found that the demographic capabilities of Campylobacter, such as mortality and transmission, could not explain the broad biodiversity of sequence types seen, suggesting that external factors such as host‐bird health and seasonality are important elements in maintaining biodiversity of Campylobacter sequence types.

Heterogeneity in Reports of Dementia Disease Duration and Severity: A Review of the Literature

BACKGROUND

The burden of dementia is changing due to population aging and changes in incidence and risk factor profiles. Reliable projections of future disease burden require accurate estimates of disease duration across different stages of dementia severity.

OBJECTIVE

To provide an overview of current evidence on severity stage and disease duration in patients with dementia.

METHODS

We reviewed the literature on duration of mild cognitive impairment (MCI), dementia, and various dementia severity stages. Data on study setting, country, sample size, severity stages, dementia type, and definition of disease duration was collected. Weighted averages and Q-statistics were calculated within severity stages and duration definitions.

RESULTS

Of 732 screened articles, 15 reported the duration of one or more severity stages and only half of those reported severity stage onset to conversion to the following stage. In those studies, MCI, very mild dementia, and mild dementia stages lasted 3-4 years and moderate and severe dementia stages lasted 1-2 years. Information on the disease duration was reported in 93 (13%) of screened articles and varied from 1 to 17 years. Reporting of dementia severity stage and disease duration in the literature was highly heterogeneous, which was accounted for only in part by dementia type, study setting, or continent of data collection.

CONCLUSION

The duration of dementia disease stages shortens with advancing stage. However, reliable modelling of future dementia burden and informing of intervention strategies will require more consistently reported duration estimates from studies that follow individuals longitudinally throughout their entire disease course.

A review and agenda for integrated disease models including social and behavioural factors

Social and behavioural factors are critical to the emergence, spread and containment of human disease, and are key determinants of the course, duration and outcomes of disease outbreaks. Recent epidemics of Ebola in West Africa and coronavirus disease 2019 (COVID-19) globally have reinforced the importance of developing infectious disease models that better integrate social and behavioural dynamics and theories. Meanwhile, the growth in capacity, coordination and prioritization of social science research and of risk communication and community engagement (RCCE) practice within the current pandemic response provides an opportunity for collaboration among epidemiological modellers, social scientists and RCCE practitioners towards a mutually beneficial research and practice agenda. Here, we provide a review of the current modelling methodologies and describe the challenges and opportunities for integrating them with social science research and RCCE practice. Finally, we set out an agenda for advancing transdisciplinary collaboration for integrated disease modelling and for more robust policy and practice for reducing disease transmission.

Climate influence the human leptospirosis cases in Brazil, 2007-2019: a time series analysis

BACKGROUND

Human leptospirosis is responsible for great losses and deaths, especially in developing countries, which can be mitigated by knowing the correct health indicators and climate influence on the disease.

METHODS

Leptospirosis cases and deaths, population and precipitation were recovered from different databases (2007-2019). Annual incidence, mortality and case fatality rates (CFRs) of human leptospirosis and average precipitation were calculated for Brazil and its regions. Time series analysis using an moving average with external variable (ARMAX) model was used to analyse the monthly contribution and precipitation influence over leptospirosis cases for each Brazilian region and for the whole country. A forecast model to predict cases for 2020 was created for Brazil.

RESULTS

Human leptospirosis exhibited heterogeneous distribution among Brazilian regions, with most cases occurring during the rainy season and precipitation influenced the disease occurrence in all regions but the South. The forecast model predicted 3276.99 cases for 2020 (mean absolute percentage error 14.680 and root mean square error 53.013). Considering the annual average for the period, the leptospirosis incidence was 1913 cases per 100 000 inhabitants, mortality was 0.168 deaths per 100 000 inhabitants and the CFR was 8.83%.

CONCLUSIONS

The models built can be useful for planning leptospirosis surveillance and control actions for the whole country and its regions and, together with the health indicators, revealed no uniform epidemiological situation of leptospirosis in Brazil.

Mathematical modeling of the SARS-CoV-2 epidemic in Qatar and its impact on the national response to COVID-19

BACKGROUND

Mathematical modeling constitutes an important tool for planning robust responses to epidemics. This study was conducted to guide the Qatari national response to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemic. The study investigated the epidemic's time-course, forecasted health care needs, predicted the impact of social and physical distancing restrictions, and rationalized and justified easing of restrictions.

METHODS

An age-structured deterministic model was constructed to describe SARS-CoV-2 transmission dynamics and disease progression throughout the population.

RESULTS

The enforced social and physical distancing interventions flattened the epidemic curve, reducing the peaks for incidence, prevalence, acute-care hospitalization, and intensive care unit (ICU) hospitalizations by 87%, 86%, 76%, and 78%, respectively. The daily number of new infections was predicted to peak at 12 750 on May 23, and active-infection prevalence was predicted to peak at 3.2% on May 25. Daily acute-care and ICU-care hospital admissions and occupancy were forecast accurately and precisely. By October 15, 2020, the basic reproduction number R0 had varied between 1.07-2.78, and 50.8% of the population were estimated to have been infected (1.43 million infections). The proportion of actual infections diagnosed was estimated at 11.6%. Applying the concept of Rt tuning, gradual easing of restrictions was rationalized and justified to start on June 15, 2020, when Rt declined to 0.7, to buffer the increased interpersonal contact with easing of restrictions and to minimize the risk of a second wave. No second wave has materialized as of October 15, 2020, five months after the epidemic peak.

CONCLUSIONS

Use of modeling and forecasting to guide the national response proved to be a successful strategy, reducing the toll of the epidemic to a manageable level for the health care system.

Development and dissemination of infectious disease dynamic transmission models during the COVID-19 pandemic: what can we learn from other pathogens and how can we move forward?

The current COVID-19 pandemic has resulted in the unprecedented development and integration of infectious disease dynamic transmission models into policy making and public health practice. Models offer a systematic way to investigate transmission dynamics and produce short-term and long-term predictions that explicitly integrate assumptions about biological, behavioural, and epidemiological processes that affect disease transmission, burden, and surveillance. Models have been valuable tools during the COVID-19 pandemic and other infectious disease outbreaks, able to generate possible trajectories of disease burden, evaluate the effectiveness of intervention strategies, and estimate key transmission variables. Particularly given the rapid pace of model development, evaluation, and integration with decision making in emergency situations, it is necessary to understand the benefits and pitfalls of transmission models. We review and highlight key aspects of the history of infectious disease dynamic models, the role of rigorous testing and evaluation, the integration with data, and the successful application of models to guide public health. Rather than being an expansive history of infectious disease models, this Review focuses on how the integration of modelling can continue to be advanced through policy and practice in appropriate and conscientious ways to support the current pandemic response.

An epidemiological model for SARS-CoV-2

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Four transmission pathways are considered in an epidemic model for SARS-CoV-2.

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The endemic steady-state and conditions for eradication are analytically derived.

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The model gives realistic values for R0 and the proportion of asymptomatic carriers.

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Simulations show that the disease can persist after an oscillatory transient.

The spread of SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) is here investigated from an epidemic model considering four pathways of person-to-person transmission. These pathways represent the propagation of this novel coronavirus by asymptomatic and symptomatic infected individuals. In this work, analytical expressions for the disease-free and endemic steady-states are derived. Also, the conditions for eradication of this contagious disease are determined. By taking into account realistic parameter values, the proposed model shows an oscillatory convergence to the endemic steady-state, which means the occurrence of a sequence of peaks in the number of sick individuals as time passes. These results are discussed from a public health standpoint.