Lukas Wittmann

I'm a passionate theoretical scientist who finds joy in developing theories and algorithms that try to capture the complex physical nature of chemistry.

SRIVD-Model With Vaccinations And Vaccination Breakthrough

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Lukas Wittmann

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Development of a Python program for investigation of epidemic developement

Introduction


With the idea of wanting insight into the pandemic with the possibility of vaccination breakthroughs, I developed an advanced version of the SRIVD-model. For this, the following iterative algorithm was created:

(1)   \begin{gather*}S[i] = S[i-1] + (- ((\beta[i-1] * I[i-1] * S[i-1]) / (N)) + \sigma[i-1] * R[i-1] - \alpha[i-1] * S[i-1]) * dt\\I[i] = I[i-1] + (((\beta[i-1] * I[i-1] * S[i-1]) / (N)) - \gamma[i-1] * I[i-1] - \delta[i-1] * I[i-1]) * dt\\R[i] = R[i-1] + (\gamma[i-1] * I[i-1] - \sigma[i-1] * R[i-1]) * dt\\V[i] = V[i-1] + (\alpha[i-1] * S[i-1]) * dt\\D[i] = D[i-1] + (\delta[i-1] * I[i-1]) * dt \end{gather*}

For this, the following variables were used:

  • Rate of infection \beta
  • Recovery rate \gamma
  • Death rate \delta
  • Vaccination rate \alpha
  • Susceptibility rate (recovered to susceptible) \sigma
  • Rate of infection for vaccinated \beta_v
  • Recovery rate for vaccinated \gamma_v
  • Death rate for vaccinated \delta_v
  • Susceptibility rate – vaccinated to susceptible \sigma_v

Below, there is a scheme which describes the above equations and my idea.

Github

This Project uses a basic SIR (susceptible, infected, recovered) model to describe epidemics and extends this model to be able to describe systems with vaccinations and possibily death. It aims to solve the equations necessary and apply them to a two-dimensional cellular automaton.
https://github.com/lukaswittmann/epidemic-simulation-model
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Simulations

It is a lot of fun to just play around with the parameters.
Important: All parameters and ratios I used are made up. I used those, because they seemed somewhat realistic in certain scenarios and show interesting behaviour in the simulations.