This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations. Based on the method of Lyapunov functions, Razumikhin technique and mathematical induction, several stability criteria are obtained for differential equations with delayed impulses. Our results show that some systems with delayed impulses may b...

Respiratory Syncytial Virus (RSV) is an acute respiratory infection that infects millions of children and infants worldwide. Recent research has shown promise for the development of a vaccine, with a range of vaccine types now in clinical trials or preclinical development. We extend an existing mathematical model with seasonal transmission to include vaccination. We model vaccination both as a ...

*Correspondence: [email protected] 1Department of Mathematics, Texas A&M University-Kingsville, Kingsville, 78363, USA Full list of author information is available at the end of the article Abstract Impulsive differential equations with impulses occurring at random times arise in the modeling of real world phenomena in which the state of the investigated process changes instantaneously at uncer...

Sufficient conditions are obtained for every solution of first order nonlinear neutral delay forced impulsive differential equations with positive and negative coefficients tends to a constant as t ∞.

This paper investigates synchronization problem of nonlinearly coupled dynamical networks, and an effectively impulsive control scheme is proposed to synchronize the network onto the objective state. Based on the stability analysis of impulsive differential equations, a low-dimensional sufficient condition is derived to guarantee the exponential synchronization in virtual of average impulsive i...