SRIVD-Model With Vaccinations And Vaccination Breakthrough


Development of a Python program for investigation of epidemic developement


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.



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.

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