Some results in Floquet theory, with application to periodic epidemic models

Analytical solutions of the simplified Mathieu’s equation

“…In this particular case it is known an analytical explicit solution (x, u) T . In order to find the expression of the characteristic coefficient, [8], [9], it was imposed an explicit necessary improper integral condition. So it was found the explicit analytical formula for the characteristic coefficient of one particular two-order differential system.…”

A Note on Uniform Exponential Stability of Linear Periodic Time-Varying Systems

“…Colaneri [5] addresses a few theoretical aspects of LPTV systems and methodology which can be useful to characterize and extend other concepts usually exploited in the time-invariant case only. On the other hand, relating computational and numerical aspects, in [26], the FCEs are directly calculated for the special types of system matrices, when the coefficient matrices are triangular. In [13], based on the solution of linear differential Lyapunov matrix equation, necessary and sufficient numerical conditions for asymptotic stability of LTV systems are given.…”

Some results on Riccati equations, Floquet theory and applications

“…Many epidemic models have been published, but Codeço [1] was the first to explicitly incorporate bacterial dynamics into a SIR epidemiological model. The following new model is a significant extension of Codeço's model [1] that incorporates the phage dynamics and the seasonal oscillation of cholera transmission, as proposed in [8]:…”