Lina Aryati

The Dynamics of HPV Infection and Cervical Cancer Cells

The development of cervical cells from normal cells infected by human papillomavirus into invasive cancer cells can be modeled using population dynamics of the cells and free virus. The cell populations are separated into four compartments: susceptible cells, infected cells, precancerous cells and cancer cells. The model system of differential equations also has a free virus compartment in the system, which infect normal cells. We analyze the local stability of the equilibrium points of the model and investigate the parameters, which play an important role in the progression toward invasive cancer. By simulation, we investigate the boundary between initial conditions of solutions, which tend to stable equilibrium point, representing controlled infection, and those which tend to unbounded growth of the cancer cell population. Parameters affected by drug treatment are varied, and their effect on the risk of cancer progression is explored.

The fundamental properties of quasi-semigroups

In this paper we focus on the abstract Cauchy problems of the time-dependent evolution equation = A(t)x(t). If the operator A(t) is time-independent, we can use the C 0-semigroups theory to solve the abstract Cauchy problem. In this case A is a infinitesimal generator of the C 0-semigroups. However, if A(t) is time-dependent, we can not apply directly the C 0-semigroups theory to solve the problem. In this situation we can use the quasi semigroups theory as development of the two parameters semigroups. This semigroups is induced by bounded evolution operators U(t, s) that satisfy some assumptions. In this paper we determine the fundamental properties of the quasi semigroups included its generator related to the time-dependent evolution equation.

Controllability and Observability of Nonautonomous Riesz-Spectral Systems

There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized) Riesz-spectral operator on a Hilbert space. The basic problems related to the equations are existence of solutions of the equations and how to control dynamical behaviour of the equations. In contrast to the autonomous control problems, theory of controllability and observability for the nonautonomous systems is less well established. In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a -quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively.