Write a function in R to simulate epidemics using the discrete time SIR model.

The function should have inputs which include the population size $($N$),$ initial conditions $($S$0,$I$0)$ and

model parameters $(\backslash$beta $,\backslash$gamma $).$

Find values of the model parameters $\backslash$beta and $\backslash$gamma that tend to produce epidemics which peak after $10$ time points and have died out by $50$ time points in a population of N $=1000$ and initial conditions S$0=999,$I$0=1($andR$0=0$ofcourse$).$

Create plots of the number of new infections $($incidence$)$ over time and the number of infectious individuals $($prevalence$)$ over time.

Use your function to simulate $100$ epidemics using the parameter values you chose above, and show the prevalence curves for these $100$ epidemics on a single plot.