Numerical study of a two-dimensional eco-epidemiological model with diffusion and convex incidence rate: Unconditionally positivity preserving method

In this paper,  a two-dimensional eco-epidemiological model with diffusion and convex incidence rate is studied, that is, the density of population depends on time and two spatial variables.  The main challenge in investigation of population models is finding a numerical method to obtain non-negative solutions. Some numerical methods, for instance Euler's method, based on the standard finite difference formulas are inefficient for solving such models because they are not always able to produce non-negative approximate solutions. On the other hand, the non-standard finite difference schemes can provide  non-negative approximations conditionally.  In { the} current work,  first, the stability of the dynamic proposed eco-epidemiological model is examined.  Then, a numerical method that provides unconditional acceptable solutions is introduced.  In what follows, the consistency and stability of the numerical method are discussed. Finally, using numerical simulation,  the efficiency of this method is compared with the Euler and non-standard methods. Furthermore, we examined the role of initial functions in interpreting species-environment interactions and deliberated on predator-prey behaviors in various scenarios.

Keywords:

Eco-epidemiological model , Convex incidence rate , Unconditionally positivity preserving method , Consistency , Stability