Steady State Solution and Stability of an Age-Structured MSIQR Epidemic Model (Report‪)‬

1. Introduction In recent years there has been increasing interest in the use of mathematical models for the analysis of real life epidemics. The need for accurate modelling of the epidemic process is vital, particularly because the financial consequences of infection disease outbreaks are growing. Two important recent examples are the 2001 foot and month disease outbreak in the UK [1] and the Severe Acute Respiratory Syndrome (SARS) epidemic in 2003 [2,3]. The fundamental model of the spread of epidemic desease was first derived by Kermack and MacKendrick [4] who studied the epidemic dynamics of an infectious disease in a population. In that model it is assumed that the population consists of three types of individuals: susceptibles (S), infectivies (I) and removed (R). The classic SIR model has influenced the study of epedimic diseases for many years. However, the simple assumption of the SIR model restricts its application to realistic problems. In recent years there have been extensive research interests to design more realistic models, including spatial models to address the spatial heterogenity on the the spatio-temporal patterns of disease dynamics [5,6]; stochastic models to study the influence of individuals with small population numbers and/or fluctuations of environment [7,8]; epidemic models with delay to describe the waiting-time between different compartments of the system [9,10]; and multi-scale models to investigate complex systems with multi-species [11].