An epidemic model with optimal control strategies was investigated for Hepatitus C Viral disease that can be transmitted through infected individuals. In this study, we used a deterministic compartmental model for assessing the effect of different optimal control strategies for controlling the spread of Hepatitus C disease in the community. Stability theory of differential equations is used to study the qualitative behavior of the system. The basic reproduction number that represents the epidemic indicator is obtained by using the condition of endemicity. Both the local stability and global stability conditions for disease free equilibrium is established. Uniqueness of endemic equilibrium point and its global stability conditions are proved. Numerical simulation of the model showed that applying all the intervention strategies can successfully eliminate Hepatitus C viral disease from the community. Manuscript profile

In this paper, we formulated a dynamical model of COVID-19 to describe the transmission dynamics of the disease. The well possedness of the formulated model equations was proved. Both local and global stability of the disease free equilibrium and endemic equilibrium point of the model equation was established using basic reproduction number. The results show that, if the basic reproduction number is less than one then the solution converges to the disease free steady state i.e. the disease free equilibrium is asymptotically stable. The endemic states are considered to exist when the basic reproduction number for each disease is greater than one. Numerical simulation carried out on the model revealed that an increase in level of contact rate among individuals has an effect on reducing the prevalence of COVID-19 and COVID-19 disease. Furthermore, sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the transmission dynamics of COVID-19. Manuscript profile