In this paper, SEIR epidemic model is used to study Ebola transmission dynamics and compared with SIR model against World Health Organisation data from Sierra Leone. It was found that the constructed SEIR model was more representative of the situation in Sierra Leone. In addition, the impact of quarantine, vaccination and/ or both interventions on the transmission dynamics of the disease was studied. The introduction of interventions caused the disease free equilibrium to become stable. Finally, the optimal control problem was solved for the transmission dynamics of the disease using these interventions as control variables. It was observed that the best intervention strategy is to implement require a combination of both quarantine and vaccination.

This project develops the SIR model of infectious diseases and uses it to study vaccination as a control strategy used to eradicate them. Vaccination combats the disease by offering immunity against future infection. Analytic expressions are obtained for key parameters such as the minimum vaccination level required. Numerical simulations are used to illustrate the main results.

Contact tracing is a key component of successful management of COVID-19. Contacts of infected individuals are asked to quarantine, which can significantly slow down (or prevent) community spread. Contact tracing is particularly effective when infections are detected quickly, when contacts are traced with high probability, when the initial number of cases is low, and when social distancing and border restrictions are in place. However, the magnitude of the individual contribution of these factors in reducing epidemic spread and the impact of population immunity (due to either previous infection or vaccination), in determining contact tracing outputs is not fully understood. We present a delayed differential equation model to investigate how the immunity status and the relaxation of social distancing requirements affect contact tracing practices. We investigate how the minimal contact tracing efficiency required to keep an outbreak under control depends on the contact rate and on the proportion of immune individuals. Additionally, we consider how delays in outbreak detection and increased case importation rates affect the number of contacts to be traced daily. We show that in communities that have reached a certain immunity status, a lower contact tracing efficiency is required to avoid a major outbreak, and delayed outbreak detection and relaxation of border restrictions do not lead to a significantly higher risk of overwhelming contact tracing. We find that investing in testing programs, rather than increasing the contact tracing capacity, has a larger impact in determining whether an outbreak will be controllable. This is because early detection activates contact tracing, which will slow, and eventually reverse exponential growth, while the contact tracing capacity is a threshold that will easily become overwhelmed if exponential growth is not curbed. Finally, we evaluate quarantine effectiveness in relation to the immunity status of the population and for different viral variants. We show that quarantine effectiveness decreases with increasing proportion of immune individuals, and increases in the presence of more transmissible variants. These results suggest that a cost-effective approach is to establish different quarantine rules for immune and nonimmune individuals, where rules should depend on viral transmissibility after vaccination or infection. Altogether, our study provides quantitative information for contact tracing downsizing in vaccinated populations or in populations that have already experienced large community outbreaks, to guide COVID-19 exit strategies.

Ebola virus disease (EVD) is a severe, often fatal disease in humans and other non-human primates caused by infection with any of the four identified Ebola virus species of the family Filoviridae. This paper develops the SEIR and the SEIHDR epidemic models that investigate the effects of the ante-mortem contact and post-mortem contact on the spread of the disease. The reproduction number of the models are determined. The equilibria and conditions for the existence of the equilibria are also determined. The models are solved numerically and the numerical simulations implemented to elucidate various scenarios. The results of the models are then compared to WHO data of confirmed cases for the 2014 Ebola outbreak in Liberia. It is observed that the SEIHDR model agrees better with the data than the SEIR model. Moreover, a new model, the SEIQDR model (a modification of the SEIHDR Model) is formulated which incorporates quarantine as an intervention. Again, this SEIQDR model is compared to the WHO data of confirmed cases for the 2014 Ebola outbreak in Liberia. The results of the SEIQDR model is found to agree better than those of the other models especially in respect of the latter stages of the disease outbreak. Finally, the effect of vaccination on both the SEIHDR and the SEIQDR models is investigated. Different rates of vaccination using numerical simulations in order to predict the effect of vaccination on the infected individuals over time is also discussed. The SEIQDR model with vaccination indicates a lower threshold which should not be less than 25% as compared to the SEIHDR model for which vaccination should not be less than 65%. It is observed that vaccination as an additional strategy helps to control the disease more effectively.