An SEIRS epidemic with disease fatalities is introduced in a growing population (modelled as a super-critical linear birth and death process). The study of the initial phase of the epidemic is stochastic, while the analysis of the major outbreaks is deterministic. Depending on the values of the parameters, the following scenarios are possible. i) The disease dies out quickly, only infecting few...

In this paper, a SEIRS epidemic model with two delays and pulse vaccination is formulated. The pulse vaccination strategy has been applied to control the spread and transmission of an infectious disease. The global attractivity of infection-free periodic solution are explored. We show that the disease is eradicated when the basic reproduction number is less than unity.

BACKGROUND Respiratory syncytial virus (RSV) is a major cause of paediatric morbidity. Mathematical models can be used to characterise annual RSV seasonal epidemics and are a valuable tool to assess the impact of future vaccines. OBJECTIVES Construct a mathematical model of seasonal epidemics of RSV and by fitting to a population-level RSV dataset, obtain a better understanding of RSV transmi...

Since the investigation of impulsive delay differential equations is beginning, the literature on delay epidemic models with pulse vaccination is not extensive. In this paper, we propose a new SEIRS epidemic disease model with two profitless delays and vertical transmission, and analyze the dynamics behaviors of the model under pulse vaccination. Using the discrete dynamical system determined b...

We study an optimal control problem for a non-autonomous SEIRS model with incidence given by a general function of the infective, the susceptible and the total population, and with vaccination and treatment as control variables. We prove existence and uniqueness results for our problem and, for the case of mass-action incidence, we present some simulation results designed to compare an autonomo...

Pulse vaccination is an effective and important strategy for the elimination of infectious diseases. A delayed SEIRS epidemic model with pulse vaccination and varying total population size is proposed in this paper. We point out, if R* < 1, the infectious population disappear so the disease dies out, while if R(*) > 1, the infectious population persist. Our results indicate that a long period o...