 Solution

The term $\gamma n(n_0-n)$ is logistic population growth, with carrying density $n_0$ and low-density growth rate $\gamma n_0$. The cell flux is $-D_n\nabla n+\chi n\nabla C$: its first part is diffusion down the density gradient, and its second is chemotaxis toward higher chemical concentration. Taking minus its divergence gives the two transport terms. Chemical production is proportional to cell density at rate $\alpha n$, degradation is first order at rate $\beta C$, and the chemical diffuses with coefficient $D_c$. All the given positive signs correspond to growth, attraction, production, degradation and ordinary diffusion respectively.