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In this paper, we propose a mathematical model to describe the transmission dynamics of infectious diseases with targeted antiviral prophylaxis strategy. Our model incorporates seasonal driving force since seasonal force has a great effect on the spread of infectious diseases. Based on the local stability of disease free equilibrium we derive the control reproduction number $\mathcal R_0$. Sufficient conditions for the global stability of the disease free equilibrium are obtained. Using the persistence theory for discrete dynamical system, we prove that the infectious disease will remain endemic if \mathcal R_0>1$. Simulation results are also provided to study the effect of targeted antiviral prophylaxis on transmission dynamics of infectious disease and investigate the influence of seasonality on the efficiency of targeted antiviral prophylaxis strategy. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to determine an optimal treatment strategy using interferon and ribavirin, through mathematical modeling. We formulate a mathematical model using a system of ordinary differential equations, which describes the interaction of target cells (hepatocytes), infected cells, infectious virions, non-infectious virions and the two drugs, namely, interferon and ribavirin. We solve an optimal control problem with an objective functional that minimizes the viral load as well as the side effects of treatment. Finally we derive optimal treatment strategy and then solve it numerically. [ABSTRACT FROM AUTHOR]

In this paper, neglecting the effects of free virus, we consider a simple model of cell-to-cell spread of HIV-1. We discuss the impact of the CD8+ cell non-cytotoxic anti-viral response (CNAR) and cytotoxic T lymphocyte (CTL) activity on infection by HIV-1. Two types of models are considered: the ordinary differential equation (ODE) model and the discrete time delay differential equation (DDE) system. The steady states of the ODE model are globally asymptotically stable respectively under two threshold criteria. In the DDE model, the global stability of the infected steady state of the ODE model becomes only ultimately stable. Moreover, at a certain interval of the time delay, the DDE model will produce Hopf bifurcation or periodic solutions. The introduction of CTL and CNAR will change the values of these steady states and induce fluctuations in the cell concentration. It also affects the critical value of the time delay and is of utility in the interpretation of typical HIV-dynamics data resulting from clinical trials. The DDE model produces sustained infective oscillations in some real parameter values, which is different from the result of the similar cell-free viral spread model with delay. [ABSTRACT FROM AUTHOR]