On Mathematical Structure of Time-Discrete Model for Epidemic Population Dynamics

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We proposed and mathematically analyzed some new time-discrete models with non-linear difference equations, which are derived by a mathematical modeling applied the stochastic process, in comparison to some basic time-continuous models of epidemic population dynamics with ordinary differential equations, which have been applied for many other subjects in population dynamics. Further for our new models, we can define the expected reproduction number of infectives in a natural manner, and we obtained some fundamental issues about its mathematical nature.