Journal of Mathematical Biology最新文献

Competitive exclusion principle, which states that two or more species limited by the same resource cannot coexist indefinitely, is a very common phenomenon in population dynamics. It is well-known that competitive exclusion principle occurs in deterministic competition models, diffusive competition models, and evolutionary competition models. In this paper, we consider an age-structured competition model among N species and obtain an interesting result: under suitable scaled birth and death rates, the species with the smallest maximum age always wins the competition to exclude the other species; that is, the competitive exclusion principle occurs in age-structured competition models.

Continuous time Markov chains are commonly used as models for the stochastic behavior of chemical reaction networks. More precisely, these Stochastic Chemical Reaction Networks (SCRNs) are frequently used to gain a mechanistic understanding of how chemical reaction rate parameters impact the stochastic behavior of these systems. One property of interest is mean first passage times (MFPTs) between states. However, deriving explicit formulas for MFPTs can be highly complex. In order to address this problem, we first introduce the concept of [Formula: see text] and develop theorems to determine whether certain SCRNs have this feature by studying associated graphs. Additionally, we develop an algorithm to identify, under specific assumptions, all possible coclique level structures associated with a given SCRN. Finally, we demonstrate how the presence of such a structure in a SCRN allows us to derive closed form formulas for both upper and lower bounds for the MFPTs. Our methods can be applied to SCRNs taking values in a generic finite state space and can also be applied to models with non-mass-action kinetics. We illustrate our results with examples from the biological areas of epigenetics, neurobiology and ecology.

We consider a cell population structured by a positive real number $x\in R_{+}$ , which represents the number of P-glycoproteins carried by the cell. These proteins combine two interesting properties: they are involved in the resistance of cancer cells to chemotherapy drugs, and the cells undergo frequent transfers of those proteins. In this article, we introduce a kinetic model to describe the dynamics of the cell population. We then consider an asymptotic limit of this equation: if transfers are frequent, the population can be described through a system of two coupled ordinary differential equations. Finally, we show that the solutions of the kinetic model converge to a unique steady-state in large times. The main idea of this manuscript is to combine Wasserstein distance estimates on the kinetic operator with more classical estimates on the macroscopic quantities.

Biological diffusion processes are often influenced by environmental factors. In this study, we investigate the effects of variable diffusion, which depend on the point between the departure and the arrival points, on the propagation of bistable waves. This process includes neutral, repulsive, and attractive transitions. Using singular limit analysis, we derive the equation for the interface between two stable states and examine the relationship between wave propagation and variable diffusion. In particular, when the transition probability depends on the environment at the dividing point between the departure and the arrival points, we derived an expression for the wave propagation speed that includes this dividing point ratio. More specifically, the threshold between wave propagation and conditional blocking in a one-dimensional space occurs when the transition probability is determined by a dividing point ratio of 3:1 between the departure and the arrival points. Furthermore, as an application of this concept, we consider the Aliev-Panfilov model to explore the mechanism for generating spiral patterns.

A patch network is introduced to describe the spatiotemporal dynamics of a delayed Lotka-Volterra competition model in heterogeneous environments. The species are subject to general dispersal patterns and spatial resource variation. It is shown that the model admits a positive equilibrium, and the infinitesimal generator associated with the linearized system has two pairs of purely imaginary eigenvalues when there are no losses of individuals during the dispersal. Furthermore, we study the stability of this positive equilibrium and the associated Hopf bifurcation when the dispersal rate is large. Moreover, the differences in the Hopf bifurcation values between no losses and losses of individuals during dispersal are considered in a special case.

We introduce a new quantity known as the network heterogeneity index, denoted by $H$ , to facilitate the investigation of disease propagation and population persistence in heterogeneous environments. Our mathematical analysis reveals that this index embodies the structure of such networks, the disease or population dynamics of patches, and the dispersal between patches. We present multiple representations of the network heterogeneity index and demonstrate that $H\ge 0$ . Moreover, we explore the applications of $H$ in epidemiology and ecology across various heterogeneous environments, highlighting its effectiveness in determining disease invasibility and population persistence.

Threshold control is an essential method for the targeted management of infectious diseases. Consequently, numerous non-smooth dynamic models incorporating state-dependent feedback control have been proposed and thoroughly analyzed. However, most existing studies introduce threshold policies based on homogeneous population models. To fill this gap, this study investigates the impact of population heterogeneity on the design of threshold policies. We developed a Filippov system based on an SIS-type metapopulation model, considering that interventions are triggered when the linear combination of infectious individuals in each group exceeds a critical threshold. Using a structured population with two groups as a case study, we theoretically investigated the existence of sliding regions, the existence and non-existence of pseudo-equilibria, and further analyzed the local and global stability of both pseudo-equilibria and regular equilibria. Additionally, we demonstrated the existence of boundary-node bifurcation in the proposed system as the threshold conditions vary. Furthermore, we showed that the total number of infectious individuals across all groups at the pseudo-equilibrium decreases monotonically as the weight assigned to the infections of one group for designing the threshold condition increases. This suggests that to minimize total infections during the epidemic for a fixed threshold, it is more effective to target the infectious population of a single group-often the group at higher risk of infection-to initialize and stop control measures than to consider combinations of infections across all groups. Moreover, for one fixed group, the monotonicity of the total infections at the pseudo-equilibrium can switch, which is governed by a critical value. Therefore, the selection of the target group to determine the threshold policy depends on the potential control strength and the local characteristics of the population groups.

Infectious disease modeling and forecasting have played a key role in helping assess and respond to epidemics and pandemics. Recent work has leveraged data on disease peak infection and peak hospital incidence to fit compartmental models for the purpose of forecasting and describing the dynamics of a disease outbreak. Incorporating these data can greatly stabilize a compartmental model fit on early observations, where slight perturbations in the data may lead to model fits that forecast wildly unrealistic peak infection. We introduce a new method for incorporating historic data on the value and time of peak incidence of hospitalization into the fit for a Susceptible-Infectious-Recovered (SIR) model by formulating the relationship between an SIR model's starting parameters and peak incidence as a system of two equations that can be solved computationally. We demonstrate how to calculate SIR parameter estimates - which describe disease dynamics such as transmission and recovery rates - using this method, and determine that there is a noticeable loss in accuracy whenever prevalence data is misspecified as incidence data. To exhibit the modeling potential, we update the Dirichlet-Beta State Space modeling framework to use hospital incidence data, as this framework was previously formulated to incorporate only data on total infections. This approach is assessed for practicality in terms of accuracy and speed of computation via simulation.

The Sterile Insect Technique (SIT) is a biological control method used to reduce or eliminate pest populations or disease vectors. This technique involves releasing sterilized insects that, upon mating with the wild population, produce no offspring, leading to a decline or eventual eradication of the target species. We incorporate a spatial dimension by modeling the pest/vector population as being distributed across multiple patches, with both wild and released sterile insects migrating between these patches at predetermined rates. We mainly focus on a two-patch system. This study has two primary objectives: first, to derive sufficient conditions for achieving the elimination of the wild population through SIT, whether releases occur in one patch or in both patches. In particular, we provide an estimate of the minimal release rates to reach elimination thanks to the diffusion rates between patches. This is the first time that such a result is given in a general manner. Second, we study an optimal SIT control strategy, where we minimize the total amount of sterile insects to release, and show that, within one patch, it can successfully reduce the wild population in that patch to a desired level within a finite time frame, provided that the migration rates between patches are sufficiently low. Numerical simulations are employed to illustrate these results and further analyze the outcomes.