def SIRmodel(v, t, N, beta, gamma):
    """Determines three differential equations of the SIR model depending on initial
    conditions and chosen parameters. dSdt determines the rate of change of
    those that are not infected but are susceptible to being infected. dIdt 
    determines the rate of change of the total infected individuals. dRdt
    determines the rate of change of the individuals who have recovered.
    
    Paramaters:
    v - vector of integers
    t - numeric sequence of form np.linspace(start, end, number of breakpoints)
    N - integer
    beta - float
    gamma - float
    
    Returns:
    Tuple of 3 floats, the change in the values of the differential 
    equations of the model at one instant in time
    """
    S, I, R = v
    dSdt = (-1 * beta * S * I) / N
    dIdt = (beta * S * I / N) - (gamma * I)
    dRdt = gamma * I
    return dSdt, dIdt, dRdt