Simulations on a Mathematical Model of Dengue Fever with a Focus on Mobility

Dengue fever is a major public health threat, especially for countries in tropical climates. In order to investigate the spread of dengue fever in neighboring communities, an ordinary differential equation model is formulated based on two previous models of vector-borne diseases, one that specifically describes dengue fever transmission and another that incorporates movement of populations when describing malaria transmission. The resulting SIR/SI model is used to simulate transmission of dengue fever in neighboring communities of differing population size with particular focus on cities in Sri Lanka. Models representing connections between two communities and among three communities are investigated. Initial infection details and relative population size may affect the dynamics of disease spread. An outbreak in a highly populated area may spread somewhat more rapidly through that area as well as neighboring communities than an outbreak beginning in a nearby rural area

A computational investigation of the ventilation structure and maximum rate of metabolism for a physiologically based pharmacokinetic (PBPK) model of inhaled xylene

Physiologically based pharmacokinetic (PBPK) models are systems of ordinary differential equations that estimate internal doses following exposure to toxicants. Most PBPK models use standard equations to describe inhalation and concentrations in blood. This study extends previous work investigating the effect of the structure of air and blood concentration equations on PBPK predictions. The current study uses an existing PBPK model of xylene to investigate if different values for the maximum rate of toxicant metabolism can result in similar compartmental predictions when used with different equations describing inhalation. Simulations are performed using values based on existing literature. Simulated data is also used to determine specific values that result in similar predictions from different ventilation structures. Differences in ventilation equation structure may affect parameter estimates found through inverse problems, although further investigation is needed with more complicated models

Computational Sensitivity Analysis on a Mathematical Model of Epileptic Seizures

Temporal lobe epilepsy is a serious neurological disorder characterized by complex partial seizures, which are thought to originate in the hippocampus.  Ordinary differential equation modeling has been used to describe changes in membrane potential of excitatory and inhibitory cells in order to gain insight into seizure propagation.  In the current study, a system of ordinary differential equations based on previous modeling is used with distinct biologically reasonable values for membrane capacitance in order to determine model sensitivity to that parameter. Because delay differential equations are used in the model, sensitivity is investigated computationally by examining the variation in output relative to various inputs. Membrane capacitance was found to affect model predictions and whether groups of cells exhibited the same behavior after a certain period of time.  Hence, membrane capacitance is a critical parameter when modeling changes in membrane potential and should be incorporated clearly.  Changes in model output as a result of changes in a time delay parameter are also investigated