First we model the epidemiology of Hepatitis E, an environmentally transmitted viral infection. The dynamics of the disease are an SEIR framework, i.e. Susceptible, Exposed, Infectious and Recovered. Hepatitis E virus is mainly spread by the fecal-oral route. This results either from directly touching the contaminated environment and eat without washing hands, or drinking contaminated water. In Kitgum district Uganda, most people live in internally displaced camps. The number of latrines in the area are not enough for the entire population, [11] , and people use the local environment for this purpose. When rain falls, it washes the faeces into water bodies. In the Kitgum region, few people have access to clean bore hole water [11] , and therefore collect water from the contaminated water sources. To model this phenomenon we use l, to denote the proportion of households in Kitgum with access to latrines. Therefore, the rate of change of contamination c of the environment is given by