In this paper, the global analysis of a HCV model with CTLs, antibody responses and therapy is studied. We incorporate into our model two treatments; the aim of the first one is to reduce the infected cells, while the second is to block the virus. We prove that the solutions with positive initial conditions are all positive and bounded. Moreover, we establish by using some appropriate Lyapunov functions that with the therapy the model becomes more stable than the one without treatment.
The mathematical model of the human immunodeficiency virus (HIV) pathogenesis with the adaptive immune response, two saturated rates and therapy is presented and studied in this work. The adaptive immune response is represented by the cytotoxic T-lymphocytes (CTL) cells and the antibodies; the two saturated rates describe the viral infection and the CTL proliferation. Two kinds of treatments are incorporated into the model; the objective of the first one is to reduce the number of infected cells, while the aim of the second one is to block the free viruses. The positivity and boundedness of solutions are established. The local stability of the disease free steady state and the infection steady states are studied. Numerical simulations are performed to show the behavior of solutions and the effectiveness of the incorporated therapy in controlling the HIV replication which can improves significantly the patient's life quality.
In this paper, we present the global analysis of a mathematical model describing and modeling the transmission of Hepatitis C Virus(HCV) infection among injecting drug users with a possible vaccination. We prove that disease will die out if the basic reproduction number R 0 ≤ 1 while the disease becomes endemic if R 0 > 1.
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