Abstract
In this paper, we first propose a diffusive pathogen infection model
with general incidence rate which incorporates cell-to-cell
transmission. By applying the theory of monotone dynamical systems, we
prove that the model admits the global threshold dynamics in terms of
the basic reproduction number R0, which is defined by
the spectral radius of the next generation operator. Then, we derive a
discrete counterpart of the continuous model by nonstandard finite
difference scheme. The results show that the discrete model preserves
the positivity and boundedness of solutions in order to ensure the
well-posedness of the problem. Moreover, this method preserves all
equilibria of the original continuous model. By constructing appropriate
Lyapunov functionals for both models, we show that the global threshold
dynamics is completely determined by the basic reproduction number.
Further, with the help of sensitivity analysis we also have identified
the most sensitive parameters which effectively contribute to change the
disease dynamics. Finally, we conclude the paper by an example and
numerical simulations to improve and generalize some known results.