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A Compartmental Model of Obesity with Treatment Response and Relapse Endemic Equilibrium Analysis and Long-Term Dynamics

Abstract

In this paper, we examine the long-term dynamics of obesity under conditions of treatment response and relapse using a four-compartment dynamical model motivated by the growing use of GLP-1 receptor agonist therapy. The model is partially calibrated to Georgia Behavioral Risk Factor Surveillance System (BRFSS) data from 2011 to 2024 and reproduces the observed trends closely. We establish the existence of a unique endemic equilibrium, linking model parameters directly to long-run prevalence. Simulations show that increasing the effective treatment-transition rate on its own produces only modest reductions in prevalence. Sensitivity analysis shows that, under the baseline setting, equilibrium obesity prevalence is most strongly influenced by obesity progression and partial recovery. Under the enhanced treatment-response setting, the effective treatment-transition rate becomes the strongest negative driver, while obesity progression remains the strongest positive driver and the influence of relapse increases substantially. Improving access to GLP-1-based treatment may increase the effective treatment-transition rate, but access alone is not sufficient. Lasting reductions in prevalence also require managing relapse, so policy design needs to address adherence and long-term retention, not access alone.

Obesity Modeling, Compartmental Systems, Endemic Equilibrium, Treatment Response, Relapse Dynamics, GLP-1 Therapy, Sensitivity Analysis

Atomic Wave Simulates Black Hole Properties

Using sheets of light to corral waves of ultracold atoms, researchers have created an experimental platform for studying the event horizons of black holes.

According to theory, if a pair of mirrors facing one another is vibrated rapidly enough, the optical field between them will display black-hole-like traits, such as the equivalent of an event horizon. These conditions have not yet been realized in the lab, but now researchers have managed something similar by swapping the roles of light and matter [1]. They used sheets of light to reflect waves of ultracold atoms back and forth, creating what they call a matter-wave cavity. Vibrating the sheets of light allows them to simulate the behavior of light propagating close to a black hole, while their setup could also enable the study of many other exotic phenomena.

An optical cavity, which is formed by a pair of mirrors facing one another, offers a versatile tool for manipulating light. Vibrating one of the mirrors causes the length of the cavity to oscillate, which can alter the light’s properties. If the mirror could be made to oscillate at the cavity’s resonant frequency—which would require motion at close to the speed of light—all the light would be compressed into an extremely short, intense pulse that would bounce between the mirrors.

European orbiter detects fresh hints of volcanic activity on Mars

New evidence from gas seeping above volcanic rifts suggests Mars is not geologically dead deep inside, but merely sleeping. Fresh fissures along the Alba Mons region hint at active spots under the surface, where gases from inside the planet may be making their way up to the surface.

An international research team led by Alexander Trokhimovskiy suggests that the release of hydrogen chloride comes from hot magma beneath the surface—a sign of dormant volcanism.

The ExoMars Trace Gas Orbiter (TGO) first reported hydrogen chloride gas in the Martian atmosphere back in 2021. This gas is commonly found escaping from magmatic vents on Earth, leading researchers to wonder whether the same was happening on Mars.

Foot-stiffening socks could make walking less tiring

Human feet are much stiffer than those of other primates, which means they limit midfoot bending during walking. The evolutionary reasons for this are not entirely clear. One idea is that the features that stiffen the foot evolved to make upright walking less effortful.

To test this, Owen Beck and Hui Tang at the University of Texas at Austin developed a pair of foot-stiffening socks, as they detail in a paper published in the journal Proceedings of the Royal Society B: Biological Sciences. Along the way, they may have come up with a low-cost garment that makes walking easier.

The socks feature tightly knitted bands around the ball of the foot. When someone stands or walks, they restrict the foot from spreading out or widening under pressure, a condition known as foot splay. This, in turn, increases arch stiffness. What the researchers didn’t know, however, was whether this extra stiffness would actually conserve energy without interfering with the natural movement needed for push-off.

New research uncovers chiral topological phases in metals without structural order

Fermions are among the most important particles in physics and include both everyday electrons and more exotic variants. Chiral fermions, like gloves, come in left- and right-handed versions and were proposed over a century ago. While high-energy neutrinos—the leading candidates for massless chiral fermions—proved to have mass, nearly (semi-) metallic solid-state crystals were discovered 15 years ago to host electronic versions of massless chiral fermions.

Mice that watch fights come away battle-ready

People love to watch violent things. From slasher films to boxing, there’s some intrinsic appeal to watching people get pummeled. The dystopian thriller “Squid Game,” for instance, debuted in 2021 and in three years racked up 330 million streams totaling more than 2.8 billion hours viewed. Even monkeys pay more attention to videos of other monkeys fighting.

Now, researchers at Princeton University have found that there may be something useful gained from all this watching: being better prepared if you find yourself in a similar situation.

In a new paper, Princeton neuroscientists reveal that male mice that merely watched other males fight were better prepared fighters themselves without being any meaner or more aggressive than other mice. Their brains changed in many of the same ways, too, as those of mice with actual fighting experience.