#'
#' SIS Functions
#'
#'
SIS_y_soln = function(N, x_0, y_0, beta, gamma, t_lim, t_res){
t_seq = seq(0, t_lim, by = t_res)
y = (N*beta - gamma)*y_0/((beta*x_0 - gamma)*exp(-t_seq) + beta*y_0)
y[y < 0] = 0
y[y > N] = N
x = N - y
return(list(x = x, y = y, t = t_seq))
}
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