Different types of epidemic models Tommi Asikainen Unit I. 2 Foresight, Modelling, Behavioural Insights & Design for Policy Overview • Compartmental models • Stochastic models • Agent based models Compartmental models(Kermack, W. O.; McKendrick, A. G.) SIR model • Assume a homogenously mixing population • Divide the population into different groups • S(t) • I(t) • R(t) • Infectious process as below: In differential equation form Exact solutions exist, we need also S(0), I(0) and R(0) N = Population size β= Number of infectious contacts per timeunit ɤ = recovery rate From this basic reproduction number R0 is derived as β / ɤ Limitations and use of this SIR model • Is used for seasonal influenza, less good for pandemics • Limitations: • Does not incorporate latent / incubation period • Does not incorporate heterogenous mixing (age groups for example) • Does not incorporate pandemic situation importation of infectious cases Extension: SEIR model Λ= Birth rate β = Infection rate a = Latent to infectious rate ɤ = Recovery rate µ = Deathrate SEIR model continued SEIR model many times applied to pandemics Limitation: 1. Lack of heterogenity • Adressed later 2. Numbere of imported infectious not constant • Numeric solution by assuming time dependant importation rate (Ferguson et al. 2006) Stochastic SIR / SEIR model • The deterministic model assumes all rates are exponentially distributed • If the exponential distribution does not fit other distributions can be used • Does this matter? • Depends what you want to model • Beginning of an outbreak -> stochasticity can have a large impact • To estimate the size of a larger outbreak, the deterministic model works rather well • When are stochastic models used? • At a beginning to estimate the inputparameters (beta, gamma) needed • Approach by estimating doubling time of the epidemic (assuming proportion asymptomatic is constant) • Has been ”successfull” with H1N1pdm, covid-19 Agent based models (ABM) • Can follow groups or individuals, throughout the pandemic • Each individual assigned to household, school, workplace etc. • Can incorporate movement and travel patterns • Can provide a lot of insight on very specific interventions or places of infection • Needs a lot of inputdata, many times all data not available • Syntetic populations, generate a population based on official statistics, household size, workplace size etc. Can generate many syntetic populations and see how dependent outputs are on these Basic reproduction number R0 • How many infectious one infectious individual causes in average in a totally susceptible population • In SIR model defined as • In SEIR model defined as • Effective reproduction number Re = Realtime value of R0 • If proportion susceptible reduce or contactrates reduce -> Re reduces • Critical value Re = 1, if below epidemic in control • For covid-19 many countries try estimating this after lockdown. Heterogenity • Different age structures in the populations, how is infection spread between these? • WAIFW – matrix (Who Acquires Infection from Whom), by studying age dependent, proportion infected in a population (for example antibodies in bloodsamples) • POLYMOD project .