I have just begun studying stability of dynamic systems. I came across this model system where I have no information about the coefficients, but I assume that they are strictly positive: \begin{aligned} \dot{x} & =\lambda-d x-\beta_1 x v-\beta_2 x y-\beta_3 x w \\ \dot{w} & =\beta_1 x v+\beta_2 x y+\beta_3 x w-(b+r) w \\ \dot{y} & =r w-a y \\ \dot{v} & =k y-\mu v \end{aligned} $x(t), w(t), y(t), v(t)$ are, respectively, the concentrations of the noninfected cells, latent infected cells, productive infected cells and virus particules at time $t$.
The problem is that I want to find $R_0$ the basic reproduction number, but I don't know how. Should I use the next-generation matrix? I don't know how to use it. There are so many variables in the equations of the concentration of the infected cells. Can anybody help me please figure this out? Thank you in advance.