When looking at dI/dt we have a term gamma*I, this is the rate in which infectious become recovered.
Why is this dependent on I, the number of infectious people?
Since if you have lots infectious people, wont it take the same amount of time for them to recover as a smaller group of people? So this rate should be a constant?
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Imagine a situation where each infected individual recovered in one day. So when you have $10$ infected individuals you have $10$ recoveries in one day. But when you have $100$ infected, you have $100$ recoveries in one day. The number of recoveries per day is proportional to the number of infected individuals.
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The others have addressed the question, I just want to add to other answers. The term $1/\delta$ reflects the expected (or average) time an infected individual spend being infected. For example, for Covid-19, the expected time for a person to be infected is about 2-3 weeks. This is how you could estimate this rate, by setting 2-3 wks = $1/\delta$, then solve for $\delta$. This is all a consequence of exponential rates in differential equations (e.g. not realistic at all in the long term).
If we have $I$ infected people and the recovery rate of the disease is $\gamma$, then in one time cycle, $\gamma I$ people recover from the infection. The time required for these people to recover is constant; it's just that due to more number of people being infected, more number of people will also recover from the disease in a given duration of time.