This research is mainly about optimising compartment models for COVID-19 and then using them for different applications that can be used to consult authorities. A compartment model describes the dynamics of a disease by implementing differential equations for the different states that belong to that disease. This is done using parameters which can be estimated from actual data or can be extracted from researches done by external authorities. We begin by extending the standard compartment model to a model which is applicable to COVID-19, this extension is based on characteristics of the virus. After this extension we are going to counteract on the assumption that susceptible and infected individuals are heterogeneously in contact with each other, since social distancing and quarantine prevent these two compartments from interacting. Also, we use specific time intervals and optimise the mortality rate. After these improvements we create an external model which estimates a contact tracing queue such that authorities can forecast how many contact tracers are needed to keep the pandemic under control. Then using the implementation of this queue, another queue is made which is dependent on its own length to forecast what happens if the government is not in contact with individuals who possibly are infected with COVID-19. Then we extend the model in such a way that vaccinated individuals can be assigned to a specific compartment, and at last we create a queue as described above with this extended model.