Mathematical Modeling of Infectious Diseases Training Course

Participants can prepare and interpret epidemiological measures required for infectious disease models.

• Incidence, prevalence and cumulative incidence calculated from line-list data
• Attack rates, secondary attack rates and case fatality ratios interpreted
• Person-time denominators matched to surveillance and cohort designs
• Case definitions assessed for sensitivity, specificity and reporting consistency
• Age-standardised rates compared using direct and indirect standardisation
• Data dictionaries document variable definitions, missingness and denominator sources

Participants can explain the mechanisms that drive transmission and estimate reproduction measures appropriately.

• Basic reproduction number R0 derived from contact and infectiousness assumptions
• Effective reproduction number Rt interpreted under changing susceptibility and interventions
• Generation intervals, serial intervals and incubation periods distinguished carefully
• Contact matrices represent age-specific mixing patterns within defined population groups
• Heterogeneous susceptibility and infectiousness incorporated through stratified compartments
• Overdispersion and superspreading represented using negative binomial offspring distributions

Participants can specify and implement deterministic SIR and SEIR transmission models.

• Flow diagrams translate disease natural history into model compartments
• Difference equations implement discrete-time SIR and SEIR models
• Ordinary differential equations express continuous-time compartmental model dynamics
• Transition rates linked to durations using reciprocal-rate relationships
• Initial conditions selected from surveillance, serology and demographic evidence
• Mass-action and frequency-dependent transmission terms compared for appropriate use

Participants can organise, run and document an infectious disease modelling workflow in R.

• R project structure separates raw data, scripts, outputs and documentation
• tidyverse pipelines clean surveillance records and create analytic datasets
• deSolve solves deterministic compartmental equations with named parameters
• Functions package model equations, scenarios and plotting routines
• ggplot2 charts show incidence, prevalence and intervention trajectories clearly
• Quarto reports combine code, assumptions, figures and interpretation

Participants can calibrate a transmission model to observed epidemic data and assess parameter identifiability.

• Likelihood functions connect observed cases to model-predicted incidence
• Least-squares fitting estimates parameters from epidemic time-series data
• Maximum likelihood estimation handles Poisson and negative binomial observations
• Parameter identifiability assessed through profile likelihoods and correlation patterns
• Calibration windows selected to avoid mixing incompatible surveillance regimes
• Fit diagnostics compare observed and predicted trajectories with residual plots

Participants can quantify uncertainty and distinguish evidence-based scenarios from speculative assumptions.

• Structural uncertainty distinguished from parameter, stochastic and observation uncertainty
• Latin hypercube sampling generates parameter sets across plausible ranges
• One-way sensitivity analysis ranks assumptions by outcome influence
• Probabilistic sensitivity analysis produces prediction intervals for policy metrics
• Scenario definitions separate evidence-based assumptions from speculative futures
• Uncertainty statements pair numeric ranges with decision-relevant interpretation

Participants can identify surveillance artefacts and adjust recent incidence estimates for reporting delays.

• Reporting delays estimated from onset, specimen and notification dates
• Right truncation corrected when interpreting recent case counts
• Nowcasting reconstructs recent incidence using fitted reporting-delay distribution models
• Ascertainment changes diagnosed through testing volumes, positivity and case definitions
• Line-list quality checks detect duplicates, impossible dates and missing fields
• Syndromic, laboratory and wastewater indicators triangulated with case surveillance

Participants can estimate Rt and use it appropriately for monitoring transmission and response thresholds.

• Renewal equations estimate Rt from incidence and generation intervals
• EpiEstim settings selected for sliding windows and prior distributions
• Rt estimates interpreted alongside testing changes and reporting delays
• Credible intervals communicated without treating threshold crossings as certainties
• Subnational Rt comparisons account for sparse counts and imported cases
• Monitoring thresholds linked to pre-agreed public health actions

Participants can model random transmission variation and interpret outbreak probabilities in small populations.

• Chain-binomial models represent transmission variability within small closed populations
• Branching processes estimate extinction probabilities during early outbreaks
• Discrete-event simulation tracks individual infections, contacts and interventions
• The Gillespie algorithm simulates continuous-time stochastic compartment transitions accurately
• Stochastic outputs summarised through quantiles, exceedance probabilities and fan charts
• Random seeds and simulation runs documented for reproducibility

Participants can incorporate demographic, clinical and contact heterogeneity into transmission models.

• Age-structured SEIR models combine demographic groups with contact matrices
• School, workplace and household contacts parameterised from mixing studies
• Risk strata represent comorbidity, occupation, residence and access barriers
• Mixing reductions model distancing, closures and behavioural change
• Equity metrics compare infections, admissions and intervention coverage by group
• Stratified results avoid masking high-risk populations within aggregate estimates

Participants can represent geographic spread, mobility and local transmission variation in a model.

• Metapopulation models connect districts through commuting and mobility flows
• Gravity models approximate movement where observed mobility data are limited
• Patch-specific transmission parameters represent geographic variation in epidemic conditions
• Importation rates separate local spread from external introductions
• Spatial outputs map incidence, risk and service demand by area
• Boundary definitions align model geography with operational response jurisdictions

Participants can compare intervention packages using transparent counterfactual transmission scenarios.

• Counterfactual scenarios compare baseline transmission with intervention packages
• Vaccination models represent efficacy, uptake, waning and delivery schedules
• Non-pharmaceutical interventions parameterised through contact reductions and adherence
• Testing, isolation and treatment pathways model delays and coverage
• Trigger policies specify indicators, thresholds, actions and review periods
• Scenario assumptions record feasibility, resource constraints and behavioural responses

Participants can translate infection projections into hospital demand and surge-planning estimates.

• Hospital admission pathways link infections to beds, oxygen and staff
• Delay distributions represent onset-to-admission, length-of-stay and discharge timing
• Severity risks stratified by age, vaccination and clinical vulnerability
• ICU occupancy projections account for competing demand and capacity limits
• Queueing assumptions identify pressure points in referral and treatment pathways
• Demand forecasts converted into staffing, supplies and surge requirements

Participants can incorporate economic measures into intervention comparisons and budget discussions.

• Costing frameworks distinguish provider costs, patient costs and programme costs
• Cost-effectiveness ratios compare intervention costs with cases and deaths averted
• Quality-adjusted life years and DALYs selected for stated decision purposes
• Discount rates, perspective and time horizon documented in economic assumptions
• Budget impact analysis estimates annual spending under delivery scenarios
• Incremental analysis excludes dominated options before ranking alternatives

Participants can test model logic, assess predictive performance and document an auditable analysis.

• Verification checks equations, code logic, units and boundary conditions
• Face validation tests assumptions with epidemiologists, clinicians and operations leads
• External validation compares forecasts against withheld outbreak observations
• Cross-validation assesses predictive performance across time periods and locations
• Posterior predictive checks test whether fitted models reproduce key patterns
• Version control records model changes, inputs, results and approvals

Participants can present model findings, uncertainty and limitations clearly to non-technical decision-makers.

• Technical briefs state question, methods, assumptions, findings and limitations
• Fan charts communicate forecast ranges without false precision
• Scenario tables compare outcomes, triggers, feasibility and resource implications
• Decision logs record recommendations, evidence, dissent and approval rationale
• Risk communication separates model outputs from policy choices and values
• Reproducible reports provide auditable links between data, code and conclusions

Participants can apply ethical, privacy and governance requirements to public health modelling work.

• Data governance applies minimisation, access control, retention and audit trails
• Privacy risks assessed for small-area, linked and sensitive health records
• Ethical review considers equity, stigma, consent and unintended consequences
• Model documentation states intended use, prohibited uses and accountability
• Open science choices balance reproducibility, confidentiality and intellectual property
• Incident procedures address erroneous outputs, misuse and public correction

Participants can establish a practical workflow for recurring modelling support during an incident.

• Model workplans define decision dates, milestones, dependencies and review gates
• Rapid response workflows assign data, modelling, clinical and communications roles
• Assumption updates follow evidence triggers and documented change-control procedures
• Readiness checklists assess data feeds, computing access and approval routes
• Stakeholder briefings align model outputs with incident management cycles
• After-action reviews capture forecast performance, decisions and improvement actions

Participants can build, review and present a complete infectious disease modelling analysis for a defined public health decision.

• Decision question, population, outcomes and intervention options defined precisely
• Analytic dataset prepared with documented cleaning and denominator choices
• Appropriate transmission model specified, coded, calibrated and stress-tested
• Scenarios quantify intervention effects, uncertainty and service implications
• Technical report presents methods, findings, limitations and recommendations
• Peer review challenges assumptions, interpretation and decision usefulness
• Presentation defends recommendations before a simulated response leadership group