Thank you so much, Suwela! Making these videos helped me to process what was going on around me, and spread some understanding (as a math and physics teacher). Knowing they were helpful to others makes me very happy. Sorry I have not been as productive with videos since then. I hope you are well.
Thank you, Fatima. The dynamics will be the same whether one individual or 100 are initially infected. You can simply say "I want to study the dynamics after 100 people were infected (or after 0.00001% of the population was infected if you normalize quantities to the population size). As long as the initial infected fraction is small, the model will show exponential growth in its initial phase. Varying the initial proportion infected will simply shift the functions left or right, not changing their qualitative behavior in any significant way. This is especially easy to see if you plot the functions on log-linear axes (plotting the log of the y axis values).
@@bpatricksullivan so if I want study the dynamic after 100 people were infected . The initial infected proportion would be 100/(number of population) ??
@@bpatricksullivan please I have another question . If I want study covid 19 . beta would be 1( because the probability for a healed individual became infected is 100%, no one is excluded from being infected) is that true ? And how can we find gamma?
Can you pls explain how can we find out the best values for beta and gamma using the historical data that we have...I tried curve fitting but results were not good for some reason I didn't understand.
Isn't it wrong that we are taking infection rate to be same for the entire duration.... people are going to stop going out gradually but we aren't accounting for that reduced infection rate right?
Pushpak, it is an assumption of this very simple model that beta and gamma are constant. In a real epidemic any effective public policy changes should lower the value of beta. That is one of many modifications that can make for a more realistic model.
Because we use the previous day to project forward, we cannot project forward on the last day. Otherwise, we would be writing data into an array location that doesn't exist. That is why there is a minus 1.
