Awesome

Jan 2020

Herd Immunity Model

Model 1: Estimation of R₀

• Purpose

  • Estimate the value of basic reproduction number

• Usage

  • Download my Jupyter notebook file: Estimation of R0.ipynb.

  • R0Func() is the function that calculates the basic reproduction number. Its inputs are the number of confirm cases, the number of suspect cases, and days t since the start of the epidemic. Here, we use the December 1st, 2019 as the start of the epidemic, which is the first nCoV case reported.

• Summary

  • This study seeks to estimate the basic reproduction number by deriving R₀ from the SEIR model. As of 2020-02-14, R₀ is estimated to be 2.41.

• Model

  • <a href="https://www.codecogs.com/eqnedit.php?latex=R_0&space;=&space;1&space;&plus;&space;\lambda&space;T_G&space;&plus;&space;\rho(1&space;-&space;\rho)&space;(\lambda&space;T_G)^2" target="_blank"><img src="https://latex.codecogs.com/gif.latex?R_0&space;=&space;1&space;&plus;&space;\lambda&space;T_G&space;&plus;&space;\rho(1&space;-&space;\rho)&space;(\lambda&space;T_G)^2" title="R_0 = 1 + \lambda T_G + \rho(1 - \rho) (\lambda T_G)^2" /></a>

                   where,

                   lambda is the growth rate of estimated infectious

                   rho is the ratio of latent period over generation period.

Model 2: Forecasting Using SEIR model

• Purpose
  • Forecast the SARS-CoV-2 epidemic peak time in metropolis by applying a deterministic SEIR metapopulation transmission model
• Usage

  • Download my Jupyter notebook file: SEIR.ipynb.

  • R0Func() is the function that calculates the newest basic reproduction number given up to date statistics. Its inputs are the number of confirm cases, the number of suspect cases, and days t since the start of the epidemic. Here, we use the December 1st, 2019 as the start of the epidemic, which is the first nCoV case reported.

  • SEIR() is the epidemic model that describes the system of differential equations.

  • betaFunc() and gammaFunc() calculate the value of transmissibility and removal rate, respectively.

  • spi.odeint() solves the system of differential equations. Its inputs are the epidemic model SEIR(), initial value of susceptible, exposed, infectious, removal INI, and the number of days since the epidemic Time

  • Please note the several assumptions will limit the use of this model, for instance, assumption of consistent behaviors before and during the epidemic means that people do not implement social or non-pharmaceutical intervention.

• Summary
  • This study seeks to forecast the peak time of SARS-CoV-2 cases. We find, under the assumptions of no quaratine intervention, Wuhan reach peak infection March 3, 2020; Beijing, Shanghai, and Guangzhou would each peak infection in the middle of May.
  • Sensitivity analysis shows that reducing half of the number of catchment size and the reproductive number would reduce the magnitude of epidemic by more than 60%, while lengthening the peak to June and duration of the epidemic to August.
• Model
  • A typical SEIR (susceptible, exposed, infectious, removed) model can be described as a system of differential equations

                   <a href="https://www.codecogs.com/eqnedit.php?latex=\small&space;\frac{dS}{dt}&space;=&space;-\beta&space;frac{S(t)I(t)}{N}&space;\newline&space;\frac{dE}{dt}&space;=&space;\beta&space;\frac{S(t)I(t)}{N}&space;-&space;\alpha&space;E(t)&space;\newline&space;\frac{dI}{dt}&space;=&space;\alpha&space;E(t)&space;-&space;\gamma&space;I(t)&space;\newline&space;\frac{dR(t)}{dt}&space;=&space;\gamma&space;I(t)" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\small&space;\frac{dS}{dt}&space;=&space;-\beta&space;\frac{S(t)I(t)}{N}&space;\newline&space;\frac{dE}{dt}&space;=&space;\beta&space;\frac{S(t)I(t)}{N}&space;-&space;\alpha&space;E(t)&space;\newline&space;\frac{dI}{dt}&space;=&space;\alpha&space;E(t)&space;-&space;\gamma&space;I(t)&space;\newline&space;\frac{dR(t)}{dt}&space;=&space;\gamma&space;I(t)" title="\small \frac{dS}{dt} = -\beta \frac{S(t)I(t)}{N} \newline \frac{dE}{dt} = \beta \frac{S(t)I(t)}{N} - \alpha E(t) \newline \frac{dI}{dt} = \alpha E(t) - \gamma I(t) \newline \frac{dR(t)}{dt} = \gamma I(t)" /></a>

                   where,

                   S(t) is the number of susceptible at time t

                   E(t) is the number of exposed at time t

                   I(t) is the number of infectious at time t

                   R(t) is the number of removed, which includes the number of recovered and dead at time t

                   N(t) is the population at time t

                   N(t) = S(t) + E(t) + I(t) + R(t)

Model 3: MCMC under spatial SEIR (In progress)

• Use Metropolis-Hastings-based Markov chain Monte Carlo (MCMC) to estimate the parameters of the spatial SEIR model

Model 4: Impact on Economic Growth (In progress)

• A panel approach for external shock:
  • exploiting the dependence among cross-sectional units to construct the counterfactuals?
• IV?

Model 5: LSTM and ARIMA short-term forecasting (In progress)

Model 6: Oversea Estimation: Possibility of Recovered Back to Infectious (In progress)

Special Thanks to

• Wuhan 2020's data science team
• BlankerL's Crawler