# Mathematical within a small community and fitted the S.E.I.R.

Mathematical models of disease outbreaks can be useful analytical tools for predicting the likely effect and magnitude an epidemic can have within a population and how external factors and pressures may influence its spread. In this report we look at two different different types of modelling; deterministic and stochastic modelling. Deterministic models have precisely determined outcomes determined through studying relationships of similar previous epidemics. Should the initial data be precisely known and the model be intricate enough, the future state of a system can be predicted. Stochastic models have an element of randomisation. They include at least one term which will change every time the model is computed and so will always give different results. Both models will be used to model the 21 month Ebola outbreak on 2014-2016. The outbreak started on 2nd March, 2014 and was the worst since its discovery in 1976. During this epidemic there were 28,712 reported cases compared to just 1,716 between 1976 and 2013. This outbreak was seen to be particularly significant as it was the first time the virus had affected those in urban areas as well as rural ones. The main three countries affected were Guinea, Sierra Leone and Liberia; in this report we will only model the Ebola outbreak in Guinea as this is where the first confirmed case of Ebola was during week 9 of 2014 in the town of Macenta.Most papers on the 2014 Ebola outbreak take a deterministic approach and use the S.I.R. model, and its extensions. Leander et al focused on modelling Ebola within a small community and fitted the S.E.I.R. (Susceptible, Exposed, Infectious, Recovered) model to the information available. They compared various deterministic models in order to accurately model the transmission responses. This was similar to the efforts of Rivers et al who took initial data from the first few months and used a further extension of the S.I.R. model. The S.E.I.H.F.R. (Susceptible, Exposed, Infectious, Hopsitalised, Funeral, Recovered) model was used to predict the possible effects the outbreak could have and how different scales of intervention may affect this. The lengthy model accounted for the long burial and funeral services that occur in West Africa. Since these rituals include touching the body of the deceased and take an average of 2 days, the virus could transmit to a susceptible individual from the handling of the body of a diseased individual. However, Merler et al used a stochastic spatiotemporal model to investigate the period up until 14th August, 2014 using the Markov chain Monte Carlo (MCMC) approach and spatial spread. This is one of the few papers that tries to overcome the limitation of non-spatial approaches, they estimated the amount of meetings an exposed individual may have in hospitals, households and while participating in funerals. The stochastic model mentioned later, general individual level model, is frequently used to model the 2001 spread of the foot and mouth disease (Deardon et al) and of influenza (Malik et al). The main complication of modelling epidemiology in either a deterministic or stochastic way is the payoff between having a model intricate enough to accurately model the situation but simple enough to solve.