Global dynamics of a simple model for wild and sterile mosquitoes.

There are known methods to manage the population dynamics of wild and sterile mosquitoes by releasing genetically engineered sterile mosquitoes. Even if a two-dimensional system of ordinary differential equations is considered as a simple mathematical model for developing release strategies, fully understanding the global behavior of the solutions is challenging, due to the fact that the probability of mating is ratio-dependent. In this paper, we combine a geometric approach called the time-scale transformation and blow-up technique with the center manifold theorem to provide a complete understanding of dynamical systems near the origin.

Pharmacological interventions for preventing clotting of extracorporeal circuits during continuous renal replacement therapy.

Background: Acute kidney injury (AKI) is a major comorbidity in hospitalised patients. Patients with severe AKI require continuous renal replacement therapy (CRRT) when they are haemodynamically unstable. CRRT is prescribed assuming it is delivered over 24 hours.

The age distribution of mortality from novel coronavirus disease (COVID-19) suggests no large difference of susceptibility by age.

Among Italy, Spain, and Japan, the age distributions of COVID-19 mortality show only small variation even though the number of deaths per country shows large variation. To understand the determinant for this situation, we constructed a mathematical model describing the transmission dynamics and natural history of COVID-19 and analyzed the dataset of mortality in Italy, Spain, and Japan. We estimated the parameter which describes the age-dependency of susceptibility by fitting the model to reported data, including the effect of change in contact patterns during the epidemics of COVID-19, and the fraction of symptomatic infections.

Pharmacological interventions for preventing clotting of extracorporeal circuits during continuous renal replacement therapy.

Background: Acute kidney injury (AKI) is a major comorbidity in hospitalised patients. Patients with severe AKI require continuous renal replacement therapy (CRRT) when they are haemodynamically unstable. CRRT is prescribed assuming it is delivered over 24 hours.

Epidemic dynamics with a time-varying susceptibility due to repeated infections.

In this paper, we consider the impact of heterogeneous susceptibility on disease transmission dynamics, using a simple mathematical model formulated by a system of ordinary differential equations. Our model describes a time-varying immunity level, which is enhanced by reinfection and diminished by waning immunity. Through mathematical analysis, we show that unexpected outbreaks, called delayed outbreaks, occur even when the basic reproduction number is less than one.

Dialysate temperature reduction for intradialytic hypotension for people with chronic kidney disease requiring haemodialysis.

Background: Intradialytic hypotension (IDH) is a common complication of haemodialysis (HD), and a risk factor of cardiovascular morbidity and death. Several clinical studies suggested that reduction of dialysate temperature, such as fixed reduction of dialysate temperature or isothermal dialysate using a biofeedback system, might improve the IDH rate.

Objectives: This review aimed to evaluate the benefits and harms of dialysate temperature reduction for IDH among patients with chronic kidney disease requiring HD, compared with standard dialysate temperature.

Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods.

We consider a mathematical model describing the maturation process of stem cells up to fully mature cells. The model is formulated as a differential equation with state-dependent delay, where maturity is described as a continuous variable. The maturation rate of cells may be regulated by the amount of mature cells and, moreover, it may depend on cell maturity: we investigate how the stability of equilibria is affected by the choice of the maturation rate.

The change of susceptibility following infection can induce failure to predict outbreak potential by R₀.

Time-varying individual host susceptibility to a disease due to waning and boosting of immunity is known to induce rich long-term behavior of the disease transmission dynamics. Simultaneously, the impact of the time-varying heterogeneity of host susceptibility on the short-term behavior of epidemics is not well-studied despite the availability of a large amount of epidemiological data on short-term epidemics. This paper proposes a parsimonious mathematical model describing the short-term transmission dynamics by taking into account waning and enhancing susceptibility following the infection.

Dynamics of an ultra-discrete SIR epidemic model with time delay.

We propose an ultra-discretization for an SIR epidemic model with time delay. It is proven that the ultra-discrete model has a threshold property concerning global attractivity of equilibria as shown in differential and difference equation models. We also study an interesting convergence pattern of the solution, which is illustrated in a two-dimensional lattice.

Ultrasonography for confirmation of gastric tube placement.

Background: Gastric tubes are commonly used for the administration of drugs and tube feeding for people who are unable to swallow. Feeding via a tube misplaced in the trachea can result in severe pneumonia. Therefore, the confirmation of tube placement in the stomach after tube insertion is important.

The determinant of periodicity in Mycoplasma pneumoniae incidence: an insight from mathematical modelling.

Until the early 1990 s, incidences of Mycoplasma pneumoniae (MP) infection showed three to five year epidemic cycles in multiple countries, however, the mechanism for the MP epidemic cycle has not been understood. Here, we investigate the determinant of periodicity in MP incidence by employing a mathematical model describing MP transmission dynamics. Three candidates for the determinant of periodicity were evaluated: school-term forcing, minor variance in the duration of immunity, and epidemiological interference between MP serotypes.

On the characteristic equation λ = α1 + (α2 + α3λ)e(-λ) and its use in the context of a cell population model.

In this paper we characterize the stability boundary in the (α1, α2)-plane, for fixed α3 with −1 < α3 < +1, for the characteristic equation from the title. Subsequently we describe a nonlinear cell population model involving quiescence and show that this characteristic equation governs the (in)stability of the nontrivial steady state. By relating the parameters of the cell model to the αi we are able to derive some biological conclusions.

Transmission Dynamics and Final Epidemic Size of Ebola Virus Disease Outbreaks with Varying Interventions.

The 2014 Ebola Virus Disease (EVD) outbreak in West Africa was the largest and longest ever reported since the first identification of this disease. We propose a compartmental model for EVD dynamics, including virus transmission in the community, at hospitals, and at funerals. Using time-dependent parameters, we incorporate the increasing intensity of intervention efforts.

Global analysis for spread of infectious diseases via transportation networks.

We formulate an epidemic model for the spread of an infectious disease along with population dispersal over an arbitrary number of distinct regions. Structuring the population by the time elapsed since the start of travel, we describe the infectious disease dynamics during transportation as well as in the regions. As a result, we obtain a system of delay differential equations.

Global dynamics of two-compartment models for cell production systems with regulatory mechanisms.

We present a global stability analysis of two-compartment models of a hierarchical cell production system with a nonlinear regulatory feedback loop. The models describe cell differentiation processes with the stem cell division rate or the self-renewal fraction regulated by the number of mature cells. The two-compartment systems constitute a basic version of the multicompartment models proposed recently by Marciniak-Czochra and collaborators [25] to investigate the dynamics of the hematopoietic system.

Stability analysis of multi-compartment models for cell production systems.

We study two- and three-compartment models of a hierarchical cell production system with cell division regulated by the level of mature cells. We investigate the structure of equilibria with respect to parameters as well as local stability properties for the equilibria. To interpret the results we adapt the concept of reproduction numbers, which is well known in ecology, to stem cell population dynamics.

On the global stability of a delayed epidemic model with transport-related infection.

We study the global dynamics of a time delayed epidemic model proposed by Liu et al. (2008) [J. Liu, J.

Global stability for a class of discrete SIR epidemic models.

In this paper, we propose a class of discrete SIR epidemic models which are derived from SIR epidemic models with distributed delays by using a variation of the backward Euler method. Applying a Lyapunov functional technique, it is shown that the global dynamics of each discrete SIR epidemic model are fully determined by a single threshold parameter and the effect of discrete time delays are harmless for the global stability of the endemic equilibrium of the model.