Dynamic Transmission Model

Concept

Theoretically, Dynamic Transmission Model is a mathematical disease modelling framework that explicitly represents the transmission of infectious diseases through interactions between individuals or population groups over time. Unlike static models, it accounts for changes in infection risk resulting from interventions, behavioural change, immunity, demographic processes and pathogen dynamics. The approach is grounded in infectious disease epidemiology and dynamic systems theory and is used to estimate both direct and indirect effects, including herd immunity, within health economic evaluation.

Mathematically, Dynamic Transmission Models are most commonly represented as systems of ordinary differential equations (ODEs), difference equations or stochastic state-transition processes describing movement between epidemiological compartments. The mathematical framework estimates temporal changes in disease states, force of infection, transmission dynamics and intervention effects while allowing parameter uncertainty and population heterogeneity to be incorporated.

In practice, Dynamic Transmission Models are parameterised using epidemiological surveillance data, contact patterns, demographic information, natural history parameters and intervention characteristics. Parameters are estimated using statistical calibration, maximum likelihood estimation or Bayesian inference. The models are implemented to evaluate vaccination programmes, screening strategies, antimicrobial resistance interventions and other communicable disease policies where transmission between individuals influences both costs and health outcomes.

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Purpose

Used to evaluate interventions affecting communicable disease transmission by estimating direct and indirect health effects, disease incidence, resource use, costs and cost-effectiveness over time within dynamically interacting populations.

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Mathematical Formulae

Primary Formula

For a deterministic susceptible-infectious-recovered (SIR) transmission model:

dS/dt = ??SI/N

dI/dt = ?SI/N ? ?I

dR/dt = ?I

where:

• S = susceptible population
• I = infectious population
• R = recovered population
• N = S + I + R
• ? = transmission rate
• ? = recovery rate

Supporting Formulae

Force of infection:

? = ?I/N

Basic reproduction number:

R? = ?/?

Effective reproduction number:

R? = R?(S/N)

Related Mathematical Methods

• Ordinary differential equations
• Stochastic compartmental modelling
• Difference equation models
• Bayesian calibration
• Maximum likelihood estimation
• Markov chain Monte Carlo
• Sensitivity analysis
• Probabilistic sensitivity analysis

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Example

A vaccination programme is evaluated in a population of 100,000 individuals.

Initial conditions:

• Susceptible = 99,000
• Infectious = 1,000
• Recovery rate (?) = 0.20 per week
• Transmission rate (?) = 0.40 per week

The basic reproduction number is:

R? = 0.40/0.20 = 2.0

Following vaccination, susceptibility declines, reducing the effective reproduction number below one. The model projects fewer infections, lower treatment costs and additional quality-adjusted life-years generated through both direct protection and herd immunity. These outcomes are incorporated into the economic evaluation.

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Excel Implementation

Function	Example Formula	Health Economics Application
SUM	=SUM(B2:B4)	Calculate total population across disease compartments.
EXP	=EXP(-B2*C2)	Calculate transition probabilities from continuous-time rates.
IF	=IF(Re<1,""Controlled"",""Growing"")	Assess epidemic control under intervention scenarios.
INDEX	=INDEX(ParameterTable,MATCH(""Beta"",Names,0),2)	Retrieve transmission parameters for scenario analyses.
Solver	Optimise calibration parameters	Estimate transmission parameters by minimising calibration error against observed incidence.

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VBA (Optional)

Automate repeated simulation of transmission dynamics across intervention scenarios and export projected epidemiological and economic outcomes.

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Sources

• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed.
• Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
• NICE. Health Technology Evaluation Manual.
• ISPOR-SMDM Modeling Good Research Practices Task Force Reports.
• Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press.
• Keeling MJ, Rohani P. Modeling Infectious Diseases in Humans and Animals. Princeton University Press.