This project consists of a disease model for analyzing the spread of COVID-19.
The project intuition and parameters estimations were retrieved from the article of Christian Hubbs. For a more detailed explanation of the modeling process, please read Christian's article.
The project uses a SEIR model. The SEIR models the flow of the population between 4 states:
- Susceptible (S)
- Exposed (E)
- Infected (I)
- Recovered/Dead (R)
The model assumes that the popualtion has a fixed size and also that it's distributed between only these 4 states. Each of these variables represents the number of people in these groups. The model is governed by 4 differential equations:
- dS/dt = -rho * beta * S * I
- dE/dt = rho* beta * S * I - alpha * E
- dI/dt = alpha * E - gamma * I
- dR/dt = gamma * I
Where:
- rho: represents the social distancing effect ([0, 1]). Where 0 represents a total lockdown
- beta: the rate of spread between a susceptible and an infectious individual.
- alpha: The incupation rate. The rate of latent individuals becoming infectious (average duration of incubation is 1/alpha)
- gamma: Recovery rate. gamma = 1/D, where D is average duration of infection.
Detailed study of the distribution of each of the 4 states trough time. It's possible to observe a peak in the number of infected around the forfieth day (around 10% of the total population).
Importance of social distancing to slow the spread of the disease. The lower the value of rho (increase in social distancing), the more flatten the curve becomes.
The values of the parameters alpha, beta and gamma for COVID-19 came from:
- https://www.thelancet.com/journals/langlo/article/PIIS2214-109X(20)30074-7/fulltext
- https://arxiv.org/pdf/2002.06563.pdf
Other references: