In this report we summarise and analyse epidemic models and chemical models to study steady state conditions by establishing basic equations, scaling parameters and equations with reduced terms to explore solutions and stability. The simplest epidemic model involves only two types of population members and works on short timescales so that births and deaths are not accounted for. The next level of model is the classic SIR model which has three classes of members, but assumes that the disease spreads quickly on a short time span so that births and deaths can still be ignored. Competition models are also reviewed. In such models, there are two species competing for the same resource and we meet the ``principle of competitive exclusion''. The report analyses characteristics, behaviour, strengths and weaknesses for the various models, by using MAPLE to investigate the steady state solutions,a nd seeking limit cycles for the models.