Continuous and Reliable Discrete Models for Simultaneous Infection
AbstractIn this talk, a continuous-time model for the transmission dynamics of two differentstrains/pathogens, with possibility of simultaneous transmission, for arbitrary disease(s) is formulated. Theexistence and stability for the disease-free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE) of the model under certain conditions are presented. Furthermore, a non-standard finite-difference (NSFD) scheme is constructed based on Mickens ,  discretization framework. В It is shown that the discrete model is dynamically consistentwith the continuous-time model by replicating the basic features (such as positivity of solutions, the dissipativity ofthe system, and its inherent conservation law, equilibrium points and their stability properties) of the continuous model. Numerical simulations confirmed these properties. R.E. Mickens, Non-standard Finite Difference Models for Differential Equations, World Scientific, Singapore, 1994. В R.E. Mickens, Applications of Nonstandard Finite Difference Schemes, World Scientific, Singapore, 2000.
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