Modeling the effect of quarantine and vaccination on Ebola disease

Ebola virus infection is a severe infectious disease with the highest case fatality rate which has become the global public health treat now. What makes the disease the worst of all is no specific effective treatment available, its dynamics is not much researched and understood. In this article a new mathematical model incorporating both vaccination and quarantine to study the dynamics of Ebola epidemic has been developed and comprehensively analyzed using fractional derivative in the sense of the Caputo derivative of order alpha is an element of (0, 1]. The existence as well as nonnegativity of the solution to the model is also verified and the basic reproduction number is calculated. Besides, stability conditions are also checked and finally simulation is done using both the Euler method and one of the top ten most influential algorithms known as Markov Chain Monte Carlo (MCMC) method. Different rates of vaccination to predict the effect of vaccination on the infected individual over time and that of quarantine are discussed. The results show that quarantine and vaccination are very effective ways to control Ebola epidemic. From our study it was also seen that there is less possibility of an individual for getting Ebola virus for the second time if they survived his/her first infection. Last but not least, real data has been fitted to the model, showing that it can be used to predict the dynamic of Ebola epidemic.