Epidemiological Dynamics Simulator

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Main Findings

Frequently Asked Question No Public Health Intervention Public Health Intervention
infectious contacts to 0 indays
Days until peak of epidemic:
Number of infected on peak day:
Total deaths over 180 days:
Estimated new infected as of
Estimated new deaths as of

Estimated Development with Public Health Intervention

Estimated Development without Public Health Intervention


The objective of this simulation is to illustrate and visualize the importance of public health interventions to decrease the current rate of infectiousness. In order to accomplish this objective, we illustrate two scenarios:

  1. Public Health Intervention Scenario
  2. No Public Health Intervention Scenario

The public health intervention scenario allows for the determination of the number of days it will take to change the latest available rate of infectiousness (R0) to a value of zero. Based on this public health intervention scenario, we provide an epidemiological prediction for the next 180 days.

The no public health intervention scenario holds constant the information for the latest available rate of infectiousness.

How the Model works?

The Basic Model


\begin{align} S & = \text{Susceptible population } \\ I & = \text{Infected}\\ D & = \text{Deaths } \\ R & = \text{Recovered} \\ \rho & = \text{infectiousness/communicability period} \\ \delta & = \text{The death rate} \\ t & = \text{Time period t} \\ \tau & = \text{The rate of transmission} \\ & = \frac{(I_{t} - I_{t-1})}{(SI)_{t-1}} \\ & = \frac{\Delta I_{t}}{(SI)_{t-1}} \end{align}

The Basic Model

Defining the rate of infectiousness R0 on day zero as

\( RO = \frac{I_{t=0} - I_{t-1}}{I_{t-1}} \times \rho = \frac{\Delta I_{t=-1}}{I_{t=-1}} \times \rho \)

then the transmission rate on day zero can be alternatively written as

\( \tau_{t=0} = \frac{RO_{t=0}}{\rho S_{t-1}}\)

The public health intervention, which lets the user define the day on which R0 becomes zero, \( t_{RO=0}\), is linearly reduced as

\( \tau_{t} = \frac{RO_{t=0}}{\rho S_{t-1}} - \frac{\frac{RO_{t=0}}{\rho S_{t-1}}}{t_{RO=0}} \times t \ \forall \ t < t_{RO=0}, 0 \ otherwise\)

Confidence Intervals of Projections

The upper and lower limit of the projections were calculated on the estimated transmission rates using the country specific data for \(I_{t=-10} \) to \(I_{t=0} \), specifically

\(se(\tau)=\frac{\frac{\sum_{t=-10}^{0} (\tau_{t} - \bar{\tau})^2}{9}}{\sqrt{10}} \)


\( \bar{\tau} = \frac{\sum_{t=-10}^{0} \tau_{t}}{10}\)

Moreover, we assumed that the susceptible population during \( [-10 \leq t \leq 0]\) is equal to the respective country’s 2019 population (Source: UN Population Prospects).

The upper and lower limits for \( \tau_{t=0}\) are then \( \tau_{t=0} \pm 1.96 \times se(\tau) \).


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