The process of programmed cell death, or apoptosis, is generally characterized by distinct morphological characteristics and energy-dependent biochemical mechanisms. Apoptosis is considered a vital component of various processes including normal cell turnover, proper development and functioning of the immune system, hormone-dependent atrophy, embryonic development and chemical-induced cell death. Inappropriate apoptosis (either too little or too much) is a factor in many human conditions including neurodegenerative diseases, ischemic damage, autoimmune disorders and many types of cancer. The ability to modulate the life or death of a cell is recognized for its immense therapeutic potential. Therefore, research continues to focus on the elucidation and analysis of the cell cycle machinery and signaling pathways that control cell cycle arrest and apoptosis. To that end, the field of apoptosis research has been moving forward at an alarmingly rapid rate. Although many of the key apoptotic proteins have been identified, the molecular mechanisms of action or inaction of these proteins remain to be elucidated. The goal of this review is to provide a general overview of current knowledge on the process of apoptosis including morphology, biochemistry, the role of apoptosis in health and disease, detection methods, as well as a discussion of potential alternative forms of apoptosis.

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Apoptosis: A Review of Programmed Cell Death

A precise definition of the basic reproduction number, Ro, is presented for a general compartmental disease transmission model based on a system of ordinary dierential equations. It is shown that, if Ro 1, then it is unstable. Thus,Ro is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for Ro near one. This criterion, together with the definition of Ro, is illustrated by treatment, multigroup, staged progression, multistrain and vectorhost models and can be applied to more complex models. The results are significant for disease control.

/pdf/reproduction-numbers-and-sub-threshold-endemic-equilibria-4b4f32pm0g.pdf

Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission

Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number $R$ are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.

https://epubs.siam.org/doi/pdf/10.1137/S0036144500371907

The Mathematics of Infectious Diseases

Acute kidney injury (AKI) is a complex disorder for which currently there is no accepted definition. Having a uniform standard for diagnosing and classifying AKI would enhance our ability to manage these patients. Future clinical and translational research in AKI will require collaborative networks of investigators drawn from various disciplines, dissemination of information via multidisciplinary joint conferences and publications, and improved translation of knowledge from pre-clinical research. We describe an initiative to develop uniform standards for defining and classifying AKI and to establish a forum for multidisciplinary interaction to improve care for patients with or at risk for AKI. Members representing key societies in critical care and nephrology along with additional experts in adult and pediatric AKI participated in a two day conference in Amsterdam, The Netherlands, in September 2005 and were assigned to one of three workgroups. Each group's discussions formed the basis for draft recommendations that were later refined and improved during discussion with the larger group. Dissenting opinions were also noted. The final draft recommendations were circulated to all participants and subsequently agreed upon as the consensus recommendations for this report. Participating societies endorsed the recommendations and agreed to help disseminate the results. The term AKI is proposed to represent the entire spectrum of acute renal failure. Diagnostic criteria for AKI are proposed based on acute alterations in serum creatinine or urine output. A staging system for AKI which reflects quantitative changes in serum creatinine and urine output has been developed. We describe the formation of a multidisciplinary collaborative network focused on AKI. We have proposed uniform standards for diagnosing and classifying AKI which will need to be validated in future studies. The Acute Kidney Injury Network offers a mechanism for proceeding with efforts to improve patient outcomes.

Acute Kidney Injury Network: report of an initiative to improve outcomes in acute kidney injury

Secret History: Return of the Black Death Channel 4, 7-8pm In 1348 the Black Death swept through London, killing people within days of the appearance of their first symptoms. Exactly how many died, and why, has long been a mystery. This Secret History documentary follows experts as they pick through the evidence and reveal why the plague killed on such a scale. And they ask, what might be coming next?

Medscape

https://www.surgical.theclinics.com/article/S0039-6109(14)00065-6/pdf

Special problems in burns.

In this paper we develop previously studied mathematical models of the regulation of testosterone by luteinizing hormone and luteinizing hormone release hormone in the human body. We propose a delay differential equation mathematical model which improves on earlier simpler models by taking into account observed experimental facts. We show that our model has four possible equilibria, but only one unique equilibrium where all three hormones are present. We perform stability and Hopf bifurcation analyses on the equilibrium where all three hormones are present. With no time delay this equilibrium is unstable, but as the time delay increases through an infinite sequence of positive values Hopf bifurcation occurs repeatedly. This is of practical interest as biological evidence shows that the levels of these hormones in the body oscillate periodically. We next discuss stability of the other equilibria heuristically using analytical methods. Then we describe simulations with realistic parameter values and show that our model can mimic the regular fluctuations of the three hormones in the body and explore numerically some of our heuristic conjectures. A brief discussion concludes the paper.

/pdf/a-delay-differential-equation-mathematical-model-for-the-36k09d7m1w.pdf

A delay differential equation mathematical model for the control of the hormonal system of the hypothalamus, the pituitary and the testis in man

Tissue Repair in Models of Diabetes Mellitus

In this paper we look at an SIRS epidemiological model with vaccination. Although immunity gained by experiencing the disease is permanent, vaccine-induced immunity is only temporary and a fixed time after vaccination individuals return to the susceptible class. The model is described and equilibrium and stability results are shown. There are three possible equilibria: one where the population is extinct; a disease-free equilibrium where the population is at a steady level and a unique endemic equilibrium. Simulation confirms that although Hopf bifurcation is theoretically possible for realistic parameter values the simulations approach the unique endemic equilibrium.

Recurrent epidemic cycles in an infectious disease model with a time delay in loss of vaccine immunity

Severe burn injury results in a multifaceted physiological response that significantly alters drug pharmacokinetics and pharmacodynamics (PK/PD). This response includes hypovolemia, increased vascular permeability, increased interstitial hydrostatic pressure, vasodilation, and hypermetabolism. These physiologic alterations impact drug distribution and excretion-thus varying the drug therapeutic effect on the body or microorganism. To this end, in order to optimize critical care for the burn population it is essential to understand how burn injury alters PK/PD parameters. The purpose of this article is to describe the relationship between burn injury and drug PK/PD. We conducted a literature review via PubMed and Google to identify burn-related PK/PD studies. Search parameters included "pharmacokinetics," "pharmacodynamics," and "burns." Based on our search parameters, we located 38 articles that studied PK/PD parameters specifically in burns. Twenty-seven articles investigated PK/PD of antibiotics, 10 assessed analgesics and sedatives, and one article researched an antacid. Out of the 37 articles, there were 19 different software programs used and eight different control groups. The mechanisms behind alterations in PK/PD in burns remain poorly understood. Dosing techniques must be adapted based on burn injury-related changes in PK/PD parameters in order to ensure drug efficacy. Although several PK/PD studies have been undertaken in the burn population, there is wide variation in the analytical techniques, software, and study sample sizes used. In order to refine dosing techniques in burns and consequently improve patient outcomes, there must be harmonization among PK/PD analyses.

David G. Greenhalgh

Papers

Special problems in burns.

A delay differential equation mathematical model for the control of the hormonal system of the hypothalamus, the pituitary and the testis in man

Tissue Repair in Models of Diabetes Mellitus

Recurrent epidemic cycles in an infectious disease model with a time delay in loss of vaccine immunity

Gap analysis of pharmacokinetics and pharmacodynamics in burn patients: a review.