Stability of Integral Delay Equations and Their Application in Infectious Disease Modeling

Integral delay equations (IDE) have applications in population dynamics and epidemics, they simplify mathematical models and allow tracking the reproductive number which is used to predict how the epidemic is progressing and is a good starting point for implementing actions to reduce the number of infected people. We represent diseases with two IDE the first one with a single delay and the second one with multiple delays and pointwise constant kernels. We use necessary and sufficient stability conditions based on the delay Lyapunov matrix to analyze the stability of IDE when the reproductive number is in matrix form where the elements of such matrix represent the interactions between different groups of the population, we show that the stability results for both IDE are the same.