We study a PDE model for dynamics of susceptible-infected interactions. The dispersal of susceptibles is via diffusion and repellent taxis as they move away from the increasing density of infected. The diffusion of infected is a nonlinear, possibly degenerating term in nondivergence form. We prove the existence of so-called weak-strong solutions in 1D for a positive susceptible initial population. For dimension $N\geq 2$ and nonnegative susceptible initial density we show the existence of supersolutions. Numerical simulations are performed for different scenarios and illustrate the space-time behaviour of solutions.
|Number of pages||15|
|Journal||Advances in Mathematical Sciences and Applications|
|Publication status||Published - Nov 2019|
Bibliographical note1 figure
- 35Q92, 35K55, 92D30