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The novel coronavirus disease (namely COVID-19) has taken attention because of its deadliness across the globe, causing a massive death as well as critical situation around the world. It is an infectious disease which is caused by newly discovered coronavirus. Our study demonstrates with a nonlinear model of this devastating COVID-19 which narrates transmission from human-to-human in the society. Pontryagin's Maximum principle has also been applied in order to obtain optimal control strategies where the maintenance of social distancing is the major control. The target of this study is to find out the most fruitful control measures of averting coronavirus infection and eventually, curtailed of the COVID-19 transmission among people. The model is investigated analytically by using most familiar necessary conditions of Pontryagin's maximum principle. Furthermore, numerical simulations have been performed to illustrate the analytical results. The analysis reveals that implementation of educational campaign, social distancing and developing human immune system are the major factors which can be able to plunge the scenario of becoming infected.

Leukemia is a malignant cancer of the blood. It is the most common type of cancer in children. In this paper, a mathematical model of leukemia in terms of ordinary differential equations has been developed. We propose a model to study the spread of leukemia by considering the effect of adoptive T cell therapy. The disease dynamics are given by a system of ordinary nonlinear differential equations that describe the interaction among susceptible blood cells, infected blood cells, cancer cells, and immune cells. The model is analyzed by using the stability theory of nonlinear differential equations and numerical simulations. A major goal of this work is to determine the spread of leukemia after applying the adoptive T cell therapy. We have observed that the system is stable locally and globally if stimulation rate or antigenicity rate of immune cells is greater than a threshold value dependent on the density of immune cells in the blood. We have also observed that the external reinfusion of immune cells by adoptive T cell therapy reduces the concentration of cancer cells and infected cells in the blood, which implies that immune cells kill cancer cells after being stimulated in the body.