Abstract
A four (4) compartmental model of (S, E, I , I ) were presented to have better understanding of parameters that influence the dynamical spread of Ebola in a population. The model is analyzed for all the parameters responsible for the dynamical spread of the disease in order to find the most sensitive parameters that need to be given attention. 
 The stability of the model was analyzed for the existence of disease free and endemic equilibrium points. Basic Reproduction Number ( ) was obtained using next generation matrix method (NGM), and it is shown that the disease free equilibrium point is locally asymptotically stable whenever the basic reproduction number is less than unity i.e ( ) and unstable whenever the basic reproduction number is greater than unity ( ).The relative sensitivity indices of the model with respect to each parameter in the basic reproduction number is calculated in order to find the most sensitive parameter which the medical practitioners and policy health makers should work on in order to reduce the spread of Ebola in the population. The result shows that effective contact rate and fraction of individuals with low immunity are the most sensitive parameters in the reproduction number. Therefore, effort should be put in place so that the basic reproduction number should not be greater unity so as to prevent the endemic situation.
Highlights
INTRODUCTIONEbola hemorrhagic fever is an infectious and deadly disease that is majorly caused by infection with one of the Ebola virus species which occurred in both humans and non-humans primates (Chimpanzees, Monkeys and Gorillas)
Basic Reproduction Number ( ) was obtained using generation matrix method (NGM), and it is shown that the disease free equilibrium point is locally asymptotically stable whenever the basic reproduction number is less than unity i.e ( ) and unstable whenever the basic reproduction number is greater than unity ( ).The relative sensitivity indices of the model with respect to each parameter in the basic reproduction number is calculated in order to find the most sensitive parameter which the medical practitioners and policy health makers should work on in order to reduce the spread of Ebola in the population
Ebola hemorrhagic fever is an infectious and deadly disease that is majorly caused by infection with one of the Ebola virus species which occurred in both humans and non-humans primates (Chimpanzees, Monkeys and Gorillas)
Summary
Ebola hemorrhagic fever is an infectious and deadly disease that is majorly caused by infection with one of the Ebola virus species which occurred in both humans and non-humans primates (Chimpanzees, Monkeys and Gorillas). Ebola Virus is transmitted into human population through contacts with the blood, organs or the bodily fluids and secretions of an infected animals like chimpanzees, fruit bats, gorilla, forest antelope and porcupines found dead in the rainforest [14, 15, 16] This virus is a member of the family Filoviridae, which are the family of viruses that cause severe hemorrhagic fever (characterized by high fever, internal bleeding, hypertension and shock) in humans. Chowell et al [5] studied the basic reproduction number of Ebola and the effects of public health measures: the cases of Congo and Uganda They presented a mathematical model to study the course of the outbreaks via an SEIR (Susceptible-exposed-infected-removed) epidemic model that includes a smooth transition in the transmission rate after control interventions are put in place. A four (4) compartmental model of (S, L, I D , I U ) was presented to check the sensitive parameters on the basic reproduction number in order to have better understanding of parameters that influence the dynamical spread of Ebola
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