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Cirrhosis of liver has become life-threatening for the human being all over the world. It is the result of long-term continuous damages of the liver. In this paper, we have developed a compartmental model of liver cirrhosis to study the dynamics behavior of this chronic disease. We have formulated the model in terms of a set of nonlinear ordinary differential equations (ODEs), based on the characteristics of disease transmission. The aim of this study is to take a close look at the transmission dynamics of liver cirrhosis. The model is developed with the focus on the concentration of the basic reproduction number and related stability analysis for the disease-free and endemic equilibrium points. Finally, Numerical simulations have been performed to illustrate the disease behavior. Our analysis reveals that infected and liver cirrhotic individuals continue to grow up and the recovered individuals start to decrease as the disease transmission rate and acute infection rate increase. As a result, the disease becomes progressive. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mathematical model of unemployment is described and analyzed for reduction of unemployed persons using two controls 'creation of new vacancies' and 'skilled manpower'. For maximization of the number of employed people at the end of implemented policy, we find the control profile of two controls using Pontryagin's Maximum Principle. This study concludes two effective controls so that the number of unemployed persons at the end of implemented policies of the government is minimized while minimizing the systematic cost of policy making. Our numerical results as illustrated in the figures strongly agree with the analytical findings. [ABSTRACT FROM AUTHOR]

Advanced liver cirrhosis has become life-threatening among the non-communicable diseases nowadays. Cirrhosis, the terminal stage of liver diseases in which the liver develops scarring as a result of various long-term continuous damages. In this paper, we develop a mathematical model to study the dynamics of chronic liver cirrhosis which can be controlled by vaccination as well as treatment. We formulate a five compartmental mathematical model of liver cirrhosis in terms of a set of nonlinear ordinary differential equations (ODEs) based on the characteristics of disease transmission by introducing two control measures. We formulate this model based on the optimal control theory using Pontryagin's Maximum Principle. For this, two types of controls such as vaccination and treatment according to underlying causes are employed to control the disease or to prevent people from being infected by liver cirrhosis. Finally, Numerical simulations are performed to illustrate the results. We observe that the optimal combination of two controls must be taken into consideration in order to reduce the liver cirrhosis transmission among the population. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mathematical model of unemployment is described and analyzed for reduction of unemployed persons using two controls 'creation of new vacancies' and 'skilled manpower'. For maximization of the number of employed people at the end of implemented policy, we find the control profile of two controls using Pontryagin's Maximum Principle. This study concludes two effective controls so that the number of unemployed persons at the end of implemented policies of the government is minimized while minimizing the systematic cost of policy making. Our numerical results as illustrated in the figures strongly agree with the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a mathematical model to study the spread of leukemia and its treatment by using the most effective immunotherapy presently known as Adoptive cell transfer. The model is governed by four state variables namely; susceptible blood cells, infected blood cells, cancer cells and immune cells. The model is analyzed by using the stability theory of non-linear differential equations and numerical simulation. We calculate the basic reproduction number and the disease free equilibrium by Jacobian Matrix (JM). A major goal of this work is to determine the spread of leukemia after applying immunotherapy. We have observed the system is stable in the local and global sense if antigenicity rate of immune cells is greater than a threshold value dependent on the density of immune cells. Besides this, external infusion of immune cells reduces the concentration of cancer cells and infected cells in the blood. This implies that immune cells kill cancer cells on being stimulated and as antigenicity rate increases rate of destruction of cancer cells also increase leading to decrease in the concentration of cancer cells and infected cells in the body. [ABSTRACT FROM AUTHOR]