Here's the given equation
$\dfrac{dAS(t)}{dt} = -AS(t)$
$\dfrac{dAR(t)}{dt} = -AI(t) + AI(t)*AS(t)$
Here's what I have done:
Rearranging and integrating equation one $\dfrac{dAS(t)}{AS(t)} = -dt$
$\displaystyle∫\dfrac{dAS(t)}{AS(t)} = -∫ dt$
Then $AS(t)$ will be $AS(t) = D*\exp(-t)$
On substituting on equation two and rearranging we have,
$\dfrac{dAR(t)}{dt} + AI(t)(1 - D\exp(-t)) = 0$
I hope I am on the right track till here and it's getting messed up when I am trying to integrate. Is everything correct till here? If so please help me integrate this equation.