Objective: This study aims to investigate the mechanisms underlying the progression of hypertension and to evaluate the effectiveness of various intervention strategies. Methods: A four-state dynamic model was developed to describe the natural progression of hypertension, considering clinical variations in blood pressure, disease trajectory, and the patient's life course. Hypertension prevalence data in China from 2002 to 2018 were utilized to calibrate the model and estimate parameters using a Metropolis-Hastings Markov Chain Monte Carlo (MCMC) algorithm. The equilibrium and stability of the system were analyzed mathematically. The model was then employed to forecast future epidemiological trends in hypertension prevalence in China. Sensitivity analyses and numerical simulations were conducted to evaluate the effectiveness of diverse intervention strategies by examining changes in prevalence and disease states. Results: The model demonstrated a strong fit to the observed data (R 2 =99%). Projections indicate a concerning upward trend, with hypertension prevalence in China forecast to rise from 30.2% in 2022 to over 40% by 2045. Simulation of interventions, however, shows that reducing disease progression and enhancing regression could lower prevalence to approximately 23-29% by 2030. An integrated strategy, featuring a 60% reduction in both prehypertension and hypertension progression rates coupled with a 45% increase in prehypertension regression, would align with WHO management targets. Conclusion: The increasing prevalence of hypertension in China can be effectively mitigated by reducing disease progression rates and strengthening prehypertension management. Attaining the WHO's 2010-2030 control objectives, however, necessitates a comprehensive and coordinated set of interventions.

It is known that for RNA viruses, such as HIV and HCV, the early or acute infection period may be correlated to higher transmissibility regarding chronic or late stages. However, studies of the impact of fitness effects caused by mutations on viral particles over transmission events are lacking. Our goal is to verify whether the passing of time can change the quality of viral particles and promote impact on an epidemic. We propose to address this question through a two-level mathematical model based on RNA viral population dynamics. The first level of the model represents the intra-host viral population dynamics and the second level represents the host-to-host dynamics of transmission events. The intra-host dynamics model uses the fitness of viral particles to track the presence of highly infective particles during transmission bottlenecks. More specifically, the intra-host dynamics is described by stochastic quasispecies, based on a multivariate branching process. The host-to-host dynamics of transmission events are emulated by a putative transmission tree with a ‘host zero’ at the root and a fixed number of branches emanating from each internal node. A Monte Carlo Markov Chain strategy was adopted to explore the tree by sampling random walks along transmission chains along the tree. Viral infections of a single host and several transmission events among hosts were simulated in early and late infection stages scenarios. The results show that the early infection stages may represent a key factor in a viral epidemic. Over the evolution of the viral population within each host the mean fitness decreases due to the occurrence of mutations (most of them causing deleterious effects). Despite the small opportunity interval, early-stage transmissions could infect new hosts at a higher rate than in late stages. It was observed that a very early transmission scenario could reach a transmission chain 20 times longer than a very late transmission scenario. This indicates that the quality of the viral particles is a relevant factor for transmission events.

Calcium ([Formula: see text]) signaling is reported as a critical factor in the insulin secretion mechanism of pancreatic [Formula: see text]-cells. Further, calcium signaling also has interactions with other similar signaling systems like adenosine triphosphate (ATP) to achieve the functions of [Formula: see text]-cells. Disturbances in any of these two interactive signaling systems can cause disorders in the secretion mechanism of insulin, leading to the onset of type-2 diabetes. Therefore, this paper presents a one-dimensional spatio-temporal mathematical model designed to explore the dynamic interactions between ATP and [Formula: see text] within a pancreatic [Formula: see text]-cell. The model under consideration comprises a set of nonlinear reaction–diffusion equations governing the behavior of [Formula: see text] and ATP. The formulation of the initial and boundary conditions takes into account the physical and physiological factors associated with the [Formula: see text]-cell. Further, the model also incorporates adenosine diphosphate (ADP) production due to the hydrolysis of ATP and [Formula: see text]-dependent insulin secretion of the [Formula: see text]-cell. The numerical results are acquired through the utilization of the finite element method. The time derivative terms are resolved through the utilization of the Crank–Nicolson method. The various glycemic states caused by variational impacts of system parameters are demonstrated.

Model reduction aims to simplify complex models by decreasing the number of equations, variables, or parameters while preserving key characteristics. This approach enhances accessibility, comprehensibility, and computational efficiency, enabling a more focused analysis of relevant variables. In this study, we describe the reduction process of a population model that incorporates cancer cell differentiation and its interaction with the immune system, maintaining the fundamental dynamics and evolution of the original model. This led to a substantial reduction in variables and parameters, creating a more efficient model suitable for computational simulations, mathematical analysis, and quantitative understanding of population dynamics. Additionally, we performed a global sensitivity analysis of model parameters using the Sobol and eFast methods, revealing insights into differences and similarities in results from a biological perspective. Our findings emphasize the critical importance of understanding and controlling parameters related to the reproduction and death rates of differentiated cancer cells, as small variations in these parameters can have significant effects on model outcomes. This underscores the importance of thoroughly understanding these essential biological variables and processes in cancer treatment, as they have a significant impact on model outcomes and, consequently, on the development of more effective therapies.

A mathematical model of competition between plasmid-bearing and plasmid-free organisms for a single limiting resource in a chemostat with distinct removal rates and in the presence of an external inhibitor is analyzed. This model was previously introduced in the special case where the growth rate functions and the absorption rate of the inhibitor follow the Monod kinetics and the removal rates are the same as the dilution rate. Here, we consider the general case of monotonic growth and absorption functions, and distinct removal rates. Through the three operating parameters of the model, represented by the dilution rate, the input concentrations of the substrate and the inhibitor, we give necessary and sufficient conditions for existence and stability of all equilibria. To better understand the richness of the model’s behavior with respect to those operating parameters, we determine the operating diagram theoretically and numerically. This diagram is very useful to understand the model from both the mathematical and biological points of view.

In this paper, we propose an epidemic model of SIR type with ratio-dependent impulse control and Beddington–DeAngelis (B–D) incidence. According to the magnitude of the basic reproductive number [Formula: see text] and the relation of the endemic equilibrium [Formula: see text] and the ratio threshold [Formula: see text], dynamical analysis of the controlled system is conducted. Under the control strategy, if [Formula: see text], the solutions converge to the disease-free equilibrium. If [Formula: see text] and [Formula: see text], the impulsive system has periodic solution that is orbitally asymptotically stable, and order-[Formula: see text] periodic solution does not exist. Furthermore, if [Formula: see text] and [Formula: see text], the solution converges either to the endemic equilibrium or to a periodic solution, which is proved to be determined by the initial value. Finally, numerical simulations are performed to demonstrate the theoretical results.

In this study, we consider a mathematical model for the disease dynamics in both prey and predator by considering the Susceptible–Infected–Recovered–Susceptible (SIRS) model with the prey–predator Lotka–Volterra differential equations. Carrying capacity, predation, migration, and immunity loss are also taken into account for both species. Using the law of mass action, the physical model is transformed into a nonlinear coupled system of ODEs. The classical/integer order ODE system is then generalized through the fractal-fractional differential operators of power law and Mittag-Leffler kernels. For the model under consideration, we additionally check for positivity, boundedness, the basic reproduction number, and equilibrium points. Graphical results are obtained by use of a numerical approach, and the existence and uniqueness of the solution are also established theoretically. The graphical solutions has been displayed via 2D and 3D phase plots. It has been shown that when the fractional order reduces, the amplitude of the chaotic attractor dynamics shrinks, along with the range of limit cycles and periodic trajectories while a drop in the fractal dimension parameter causes an increase in the time period of the chaotic attractor dynamics. This study not only improves the understanding of epidemic breakouts in predator–prey systems, but also highlights the efficiency of fractal-fractional calculus in ecological modeling.

Sterile Insect Technique (SIT) is a biological insect (or pest) control tool aiming to reduce or eliminate wild insect (or pest) populations by releasing sterile insects (or pests). In this paper, we propose and study a stage- and sex-structured entomological model describing the dynamics of wild-type mosquito population and observed that the extinction equilibrium of the model is globally asymptotically stable when the basic offspring number is less than unity. However, when the basic offspring number is greater than unity, the extinction equilibrium becomes unstable, followed by the emergence of the stable interior equilibrium. We extend the model by introducing sterile male mosquitoes as a biological control agent against wild-type mosquito species. We have considered the Allee effect in the fertile female mosquito population due to the presence of non-egg-laying females in the mosquito population. While the wild mosquito-free equilibrium of the SIT model is always locally asymptotically stable, there exists either no interior equilibrium or a pair of interior equilibria, among which one is always unstable, and the other is always locally asymptotically stable. We observed that the wild mosquito population of the SIT system goes to extinction, followed by a saddle-node bifurcation when the supply rate of sterile males increases through some critical threshold value. As an alternative to the eradication policy, we formulated an optimal control problem to suppress the wild mosquito population, which suggests increasing the investment in awareness campaigns to suppress the mosquito population.

This paper proposes a two-dimensional modified Leslie–Gower predator–prey model with carry-over effects, fear, prey protection and additional food, including prey harvesting. For this, it assumes the carry-over effect with delay incorporated in the birth rate of the prey population and gestation delay in Leslie–Gower term of a predator, and supposes that the predator consumes the prey according to Holling type II functional response. This dynamical system is split into two groups, namely non-delayed and delayed systems, respectively. In the non-delayed system, first, we discuss positivity, boundedness solutions, and the existence of equilibria, especially finding the coexistence of interior equilibrium points under certain conditions. After that, local and global stabilities are systematically analyzed. In addition, we obtain the conditions of Hopf-bifurcation in terms of the growth rate of prey species, prey protection and preference rate of predator for the non-delayed system. Whereas in the delayed system, both the delays have an essential role in governing the dynamical system discussed in three cases, and each case found the Hopf-bifurcation parameters for which the system changes stability behavior into instability. At last, the numerical simulations have been carried out to verify the theoretical findings.

In this paper, we investigate the impact of catheterization on swallowing if esophagus suffers from a hiatus hernia. It is modeled as a partially diverging tube having a peripheral layer of different viscosity besides the core layer. The model duly considers mass conservation in the two layers separately. It is inferred that even in the presence of a catheter inside esophagus, any sliding herniation requires less pressure for flow, i.e., swallowing will be easier if the esophagus diverges more near the cardiac sphincter. However, the presence of a catheter requires esophagus to work more in order to swallow the same quantity. Pressure enhances by many folds, but its distribution remains similar. The time-averaged flow rate and the maximum pressure, restraining fluid from swallowing, give some clues about a catheterized herniated esophagus. The flow enhances for a thinner peripheral layer. A more viscous peripheral layer as well favors flow. However, the thickness of the catheter hinders swallowing. This is to be taken care of while a patient undergoes any catheterized treatment. Increasing wave amplitude and dilating parameters can enhance flow in the presence of a catheter. It is also concluded that the frictional forces exerted by the tube wall on the peripheral layer increase in the catheter’s presence.