Modeling Shrimp Biomass and Viral Infection for Production of Biological Countermeasures

Abstract

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.

A division-dependent compartmental model for computing cell numbers in CFSE-based lymphocyte proliferation assays

“…To better understand rates at the generation number cohort or division number cohort level, one should attempt to develop individual (cohort) dynamics to investigate the CFSE data in a Type I framework of Aggregate Data/Individual (Cohort) Dynamics inverse problems such as those discussed in [1,Chapter 14] and [5]. Similar approaches have been successfully pursued in marine and insect population models [3,6,10,12,22] as well as in physiologically based pharmacokinetics (PBPK) models in toxicology [5,17]. Fortunately, a simple reformulation of (1) allows such an approach and permits both the accurate quantification of total cells per division number and the accurate estimation of proliferation and death rates in terms of division number in such a framework.…”

Monotone approximation for a nonlinear size and class age structured epidemic model

“…A special case of the general class is the biomass/viral infection model of [6]. We believe that this method can be applied to a more generalized version of this model in which mortality rates and birth rates depend on the total population or total biomass of each state; this would yield results under even more reasonable and realistic assumptions.…”

Least Squares Estimation of Probability Measures in the Prohorov Metric Framework

“…It is commonly assumed that the states of interest for these individuals are described by a single mathematical framework, but that each individual is described by a unique set of parameters within that framework. For instance, the growth of mosquitofish [9,16,17] and shrimp [5,11,13] have been shown to be described by a size-structured partial differential equation model in which the rate of individual growth is assumed to vary probabilistically across the population. HIV replication data has been shown to be accurately described by a cellular-level model in which intracellular delays vary from cell to cell [7].…”