In this post we shall look at ways experts analyse the spread of COVID-19.
My own mathematical techniques are simple but have produced some surprising results.
Analysis can quite often involve solving systems of differential equations (see below).
How Ro is estimated
‘A typical epidemiological model by which R0 is estimated is based on three factors: individual Susceptibility to the infection, the rate at which infections actually occur (Infectivity), and the rate of Removal of infection from the population, by either recovery or death. This is the so-called S-I-R model.The model involves the solution of simultaneous linear differential equations and was described as long ago as 1927 by W. O. Kermack and A. G. McKendrick. A version of their model is shown in Figure 3.’ See:
Here is a set of differential equations for the CovidSim model. See:
There are other methods that can be used as well.
The list below is taken from the table in this article:
See the Methods Column in the table.
- Stochastic Markov Chain Monte Carlo methods (MCMC)
- Mathematical model, dynamic compartmental model with population divided into five compartments: susceptible individuals, asymptomatic
individuals during the incubation period, infectious individuals with symptoms, isolated individuals with treatment and recovered individuals
- Statistical exponential Growth, using SARS generation time=8.4 days, SD=3.8 days
- Statistical maximum likelihood estimation, using SARS generation time=8.4 days, SD=3.8 days
- Mathematical transmission model assuming latent period=4 days and near to the incubation period
- Mathematical Incidence Decay and Exponential Adjustment (IDEA) model
- Mathematical model including compartments Susceptible-Exposed-Infectious-Recovered-Death-Cumulative (SEIRDC)
- Statistical exponential growth model method adopting serial interval from SARS (mean=8.4 days, SD=3.8 days) and MERS (mean=7.6 days, SD=3.4 days)
- Mathematical model, computational modelling of potential epidemic trajectories
- Stochastic simulations of early outbreak trajectories
- Mathematical SEIR-type epidemiological model incorporates appropriate compartments corresponding to interventions
- Statistical exponential growth model
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