Numerical modeling and theoretical analysis of a nonlinear advection-reaction epidemic system.

BACKGROUND AND OBJECTIVE: Epidemic models are used to describe the dynamics of population densities or population sizes under suitable physical conditions. In view that population densities and sizes cannot take on negative values, the positive character of those quantities is an important feature that must be taken into account both analytically and numerically. In particular, susceptible-infected-recovered (SIR) models must also take into account the positivity of the solutions. Unfortunately, many existing schemes to study SIR models do not take into account this relevant feature. As a consequence, the numerical solutions for these systems may exhibit the presence of negative population values. Nowadays, positivity (and, ultimately, boundedness) is an important characteristic sought for in numerical techniques to solve partial differential equations describing epidemic models. METHOD: In this work, we will develop and analyze a positivity-preserving nonstandard implicit finite-difference scheme to solve an advection-reaction nonlinear epidemic model. More concretely, this discrete model has been proposed to approximate consistently the solutions of a spatio-temporal nonlinear advective dynamical system arising in many infectious disease phenomena. RESULTS: The proposed scheme is capable of guaranteeing the positivity of the approximations. Moreover, we show that the numerical scheme is consistent, stable and convergent. Additionally, our finite-difference method is capable of preserving the endemic and the disease-free equilibrium points. Moreover, we will establish that our methodology is stable in the sense of von Neumann. CONCLUSION: Comparisons with existing techniques show that the technique proposed in this work is a reliable and efficient structure-preserving numerical model. In summary, the present approach is a structure-preserving and efficient numerical technique which is easy to implement in any scientific language by any scientist with minimal knowledge on scientific programming.

Evaluation of the whole body physiologically based pharmacokinetic (WB-PBPK) modeling of drugs.

The Physiologically based pharmacokinetic (PBPK) modeling is a supporting tool in drug discovery and improvement. Simulations produced by these models help to save time and aids in examining the effects of different variables on the pharmacokinetics of drugs. For this purpose, Sheila and Peters suggested a PBPK model capable of performing simulations to study a given drug absorption. There is a need to extend this model to the whole body entailing all another process like distribution, metabolism, and elimination, besides absorption. The aim of this scientific study is to hypothesize a WB-PBPK model through integrating absorption, distribution, metabolism, and elimination processes with the existing PBPK model.Absorption, distribution, metabolism, and elimination models are designed, integrated with PBPK model and validated. For validation purposes, clinical records of few drugs are collected from the literature. The developed WB-PBPK model is affirmed by comparing the simulations produced by the model against the searched clinical data. . It is proposed that the WB-PBPK model may be used in pharmaceutical industries to create of the pharmacokinetic profiles of drug candidates for better outcomes, as it is advance PBPK model and creates comprehensive PK profiles for drug ADME in concentration-time plots.

On p53 revival using system oriented drug dosage design.

We propose a new paradigm in the drug design for the revival of the p53 pathway in cancer cells. It is shown that the current strategy of using small molecule based Mdm2 inhibitors is not enough to adequately revive p53 in cancerous cells, especially when it comes to the extracting pulsating behavior of p53. This fact has come to notice when a novel method for the drug dosage design is introduced using system oriented concepts. As a test case, small molecule drug Mdm2 repressor Nutlin 3a is considered. The proposed method determines the dose of Nutlin to revive p53 pathway functionality. For this purpose, PBK dynamics of Nutlin have also been integrated with p53 pathway model. The p53 pathway is the focus of researchers for the last thirty years for its pivotal role as a frontline cancer suppressant protein due to its effect on cell cycle checkpoints and cell apoptosis in response to a DNA strand break. That is the reason for finding p53 being absent in more than 50% of tumor cancers. Various drugs have been proposed to revive p53 in cancer cells. Small molecule based drugs are at the foremost and are the subject of advanced clinical trials. The dosage design of these drugs is an important issue. We use control systems concepts to develop the drug dosage so that the cancer cells can be treated in appropriate time. We investigate by using a computational model how p53 protein responds to drug Nutlin 3a, an agent that interferes with the MDM2-mediated p53 regulation. The proposed integrated model describes in some detail the regulation network of p53 including the negative feedback loop mediated by MDM2 and the positive feedback loop mediated by Mdm2 mRNA as well as the reversible represses of MDM2 caused by Nutlin. The reported PBK dynamics of Nutlin 3a are also incorporated to see the full effect. It has been reported that p53 response to stresses in two ways. Either it has a sustained (constant) p53 response, or there are oscillations in p53 concentration. The claimed dosage strategy achieves the p53 response in the first case. However, for the induction of oscillations, it is shown through bifurcation analysis that to achieve oscillating behavior of p53 inhibition of Mdm2 is not enough, rather antirepression of the p53-Mdm2 complex is also needed which leads to the need of a new drug design paradigm.