Modeling Biological Systems
The use of mathematical models provides insights into the qualitative and quantitative characteristics of certain biological systems. Its complex behavior can be described by a set of nonlinear differential equations and its corresponding dynamics can be investigated through numerical simulations. Experimental measurements and observations are needed to validate the accuracy of model predictions.
ModApp group is interested in quantifying complexities of physiological systems (e.g. cardiovascular-respiratory systems and capillary refilling); transmission dynamics of infectious diseases; theoretical modeling in ecology, stochastic epidemiology on random networks, and age-structured population.
Chemical Reaction Network Theory
A chemical reaction network is a finite collection of chemical reactions that can be viewed as interactions among entities in a system. Kinetic functions are assigned to these reactions, and correspondingly, the dynamics of the kinetic system can be described by a system of ordinary differential equations (ODEs). The evolution of the concentrations of the chemical species over time can be captured by a system of ODEs. Chemical reaction network theory (CRNT) can be used to establish results on solutions of the ODEs such as existence, parametrization, uniqueness, multiplicity, and stability of steady states. One can also investigate persistence and permanence of systems, and periodicity of solutions. CRNT may also be used in cases where parameters are not specified and there are scarcity of kinetic order values.
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In the Philippines, a team of researchers lead by Dr. Eduardo R. Mendoza focuses on the existence and parametrization of steady states, multistationarity algorithms for classes of kinetics, and decomposition theory of chemical reaction networks. These results are being applied to areas such as systems biology, chemistry, game theory and engineering. Useful areas of mathematics to study CRNT are linear algebra, graph theory and differential equations for dynamical systems. There are also directions where one uses other areas such mathematical analysis.
Applications of Optimal Control Theory in Biological Models
Optimal control theory is a branch of mathematics developed to obtain methods to control a dynamical system. It is a powerful tool that can be used to make informed decisions involving complex biological phenomena. In particular, it can be applied to determine effective and cost-efficient intervention measures to mitigate the spread of a disease. It can aid in the design of optimal therapeutic scheme in the treatment of lethal diseases like cancer.
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ModApp employs optimal control theory to describe the response of cardiovascular-respiratory system under ergometer test; examine optimal strategies to curtail transmission of infectious diseases (e.g. TB, HIV, etc.); and explore (poly)therapeutic strategies in cancer (e.g. glioblastoma, lung, etc.) treatment.
