A system of ordinary differential equations is formulated to describe the pathogenesis of HIV infection, wherein certain important features that have been shown important by recent experimental research are incorporated in the model. These include the role of CD4+ memory cells that serve as a major reservoir of latently infected cells, a critical role for T-helper cells in the generation of CD8 memory cells capable of efficient recall response, and stimulation by antigens other than HIV. A stability analysis illustrates the capability of this model in admitting multiple locally asymptotically stable (locally a.s.) off-treatment equilibria. The phenomenon of "viral blips" experienced by some patients on therapy with viral load levels suppressed below the detection limit is also investigated. Censored clinical data is used to demonstrate that this model provides reasonable fits to all the patient data available for this study and, moreover, that it exhibits impressive predictive capability. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.
In this paper we develop a mathematical model for the rapid production of large quantities of therapeutic and/or preventative countermeasures. We couple equations for biomass production with those for vaccine production in shrimp that have been infected with a recombinant viral vector expressing a foreign antigen. The model system entails both size and class-age structure.Key Words: Size/class-age structured population models, shrimp growth/viral progression dynamics, latently-acutely infected. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.
In this paper, we study a nonautonomous size and class age structured epidemic model with nonlinear and nonlocal boundary conditions. We establish a comparison principle and construct convergent monotone sequences to prove the existence of solutions. Uniqueness of solutions is also established.
We compare several approaches to uncertainty propagation that have been used in the literature to formulate the uncertainty in a dynamical system governed by ordinary differential equations. Specifically we focus on the evolution of probability density functions of the associated stochastic processes, and discuss their applications in different fields.
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