keywords: Vital Dynamics, Contact Tracing and Quarantine
This thesis extends the standard SEIR epidemiology model of Ebola virus to include both Human and Monkey population. Nine (9) compartments were considered, namely: ( ), S H susceptible Human FUW Trends in Science & Technology Journal, www.ftstjournal.com e-ISSN: 24085162; p-ISSN: 20485170; August, 2022: Vol. 7 No. 2 pp. 885-889 1203 ( ), E H individual that are suspected to have had contact with infected human and monkey ( ), I H infected Human ( ), R H Recovered Human ( ), Q H Quarantine Human and ( ), D H Dead Human. For Monkey ( ), S M Susceptible Monkey, infected Monkey and ( ), D M Dead Monkey. We mathematically modeled the natural growth, the interactions between these two populations. The disease-free equilibrium (DFE) and endemic equilibrium (EE) were established. We obtained the basic reproduction number, which can be used to control the transmission dynamics of the disease and thus, established the conditions for local and global stability of the disease free- equilibrium thus, using Routh- Hurwitz criterion and Castillo-Chavez approach respectively. The result of the analysis of the stability of the disease-free equilibrium state that Ebola can totally be eradicated if effort is made to ensure that the rate of recovery infected individuals with Ebola virus and the rate of natural death must have a lower bound. Numerical analysis for the model has done and demonstrated that in the case of patients with Ebola virus, Ebola Virus Disease will be eradicated if effort is intensified in bringing down the transmission rate of Ebola Virus.