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Corona virus disease 2019 (Covid-19) is an illness caused by a natural corona virus called severe acute respiratory syndromes corona virus 2 (SARS-COV-2 formally called Covid-19) which is respiratory illness and has been declared the Covid-19 outbreak a global pandemic by World Health Organization (WHO). Presently, Covid-19 becomes a health concern around the globe. In present article, we investigated the dynamics of Covid-19 infectious disease under the fractional order derivative from both theoretical as well as analytical aspects. Using fixed-point theory results, we developed the indispensable conditions for the existence of the solution of the proposed model. Further we have used the techniques of Laplace transform coupled with the Adomian's decomposition method to obtain the semi analytical solution for the model under consideration. Finally we have provided some graphical presentation corresponding to different fractional order derivatives via Matlab for the desired solutions. [ABSTRACT FROM AUTHOR]

In this article, the qualitative theory and approximate solutions for fractional order Ebola model via Atangana-Baleanu-Caputo (ABC) fractional operators are developed. Using various tools of analysis, the conditions for the existence and stability of the proposed model are established. With the help of Laplace Adomain Decomposition method, we obtain the approximate solutions for the said model. In the last part, using Matlab, we plotted various graphs to discuss the underlying model for different fractional order values of γ. [ABSTRACT FROM AUTHOR]

A mathematical model is used to study the dynamics of ovine brucellosis when transmitted directly from infected individual, through contact with a contaminated environment or vertically through mother to child. The model developed by Aïnsebaet al.[A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn. 4 (2010), pp. 2–11. Available athttp://www.math.u-bordeaux1.fr/∼pmagal100p/papers/BBM-JBD09.pdf. Accessed 3 July 2012] was modified to include culling and then used to determine important parameters in the spread of human brucellosis using sensitivity analysis. An optimal control analysis was performed on the model to determine the best way to control such as a disease in the population. Three time-dependent controls to prevent exposure, cull the infected and reduce environmental transmission were used to set up to minimize infection at a minimum cost. [ABSTRACT FROM PUBLISHER]