A Mathematical Analysis of an In-vivo Ebola Virus Transmission Dynamics Model

Ebola virus (EBOV) infection is a hemorrhagic and hazardous disease, which is among the most shocking threats to human health causing a large number of deaths. Currently, there are no approved curative therapies for the disease. In this study, a mathematical model for in-vivo Ebola virus transmission dynamics was analyzed. The analysis of the model mainly focused on the sensitivity of basic reproductive number,  pertaining to the model parameters. Particularly, the sensitivity indices of all parameters of  were computed by using the forward normalized sensitivity index method. The results showed that a slight change in the infection rate immensely influences  while the same change in the production rate of the virus has the least impact on . Thus, , being a determining factor  of the disease progression, deliberate control measures targeting the infection rate, the most positively sensitive parameter, are required. This implies that reducing infection rate will redirect the disease to extinction. Keywords: Ebola virus infection, immune response, sensitivity index, mathematical model

Modeling the Dynamics of Hepatitis C Virus and Immune System during Acute Infection

In this paper, a mathematical model on the interaction between hepatitis c virus (HCV) and immune system has been studied. The paper intends to upgrade the model developed by Avendano et al.(2002) by including death of hepatocytes due to infection and spontaneous clearance of viruses by a noncytolytic process during acute stage of the HCV infection. The next generation matrix method has been applied to compute the basic reproductive number. Also, the stability analysis of the system has been performed for the existence of the disease free and endemic equilibrium states using Meltzer matrix, Routh-Hurwitz and Lyapunov methods. The results indicate that the disease free equilibrium state is locally asymptotically stable if, and unstable if.The endemic equilibrium state is both locally and globally asymptotically stable. We calculated the sensitivity indices of the dynamic threshold relating to each parameter in the model, where we found that the decrease of the rate of infection and the rate of generation of virions have the effect of lessening the infection, which suggests that the disease can be controlled when therapeutic intervention is done on these parameters.Keywords: Hepatitis C virus, Immune system, Basic reproductive number, Disease-free equilibrium state, Endemic equilibrium state