Consideration on a kind of difference equations and differential equations with time delay

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We obtained a new eigenvalue algorithm based on the discrete hungry Lotka-Volterra (dhLV) system of multiplicative type and discussed its convergence with the help of the center manifold theory. Another idea to derive the conserved quantities of the dhLV system was found only using the properties of the characteristic polynomial of the corresponding matrix. Moreover, we are concerned with the discrete epidemic models with and without time delay. Applying a proper discretization, the positivity of the solution for the discrete model can be kept, and then the ultra-discretized epidemic models can be easily derived. We investigated the global properties of the solution for such ultra-discretized epidemic models.