The impact of diapause eggs on mosquito population suppression is important but has often been neglected in mathematical modeling. In this work, we establish a differential equation model to investigate the dynamical behavior of wild mosquito population under constant release of sterile mosquitoes. Our model includes the effect of diapause eggs and adopts a new expression of mosquito intraspecific competition in both larva and adult stages. By using constructive techniques, we obtain sufficient conditions for the existence and stability of periodic solutions, as well as the stability of the zero equilibrium. We explain in the Conclusion why it is difficult to completely eliminate wild mosquitoes in field trial. Numerical simulations are provided to validate our findings.

Releasing Wolbachia-infected mosquitoes to replace the wild mosquito population represents an innovative biocontrol strategy currently implemented in over 15 countries to combat mosquito-borne diseases. This study investigates the population dynamics of Wolbachia invasion under periodic release strategies where only infected males are additionally introduced to accelerate population replacement, a strategy that yields a challenging non-autonomous difference equation model. The analytical complexity stems from the infinite composition of distinct rational maps, which renders conventional methods ineffective. To address this challenge, we develop a novel framework based on Poincaré map theory and geometric analysis. Our approach identifies a critical release threshold α* that fully determines system behavior. The main result reveals a sharp dichotomy. When release ratios surpass α*, the Wolbachia-fixed equilibrium achieves global stability, guaranteeing successful population replacement. Below this threshold, the system maintains bistability. This theoretical advancement establishes a quantitative criterion for optimizing intervention strategies, resolving computational obstacles inherent in non-autonomous systems while providing practical guidance for designing effective Wolbachia-based control programs.

In this paper, we propose and investigate a hybrid mosquito population suppression model with sterile mosquitoes release depending on both the status and periodic sampling times of wild mosquitoes, which is used to mimic one of the simplest and quite practical mosquito control strategies to ensure that dengue fever outbreaks do not occur. Our analyses show that the model dynamics completely depend on the control threshold D of mosquitoes allowed in the field, below which disease outbreaks do not occur. We demonstrate that the wild mosquito population will eventually go to the maximum equilibrium when D is larger, and will go to the minimum equilibrium when D is small. In the case when D has intermediate values, we obtain an explicit sufficient condition for the existence of a unique subharmonic solution of the model with minimal period mk with the aid of the Poincar & eacute; mapping method, where m > 1 is an integer. It is thus indispensable to place D in the middle range in order to control mosquitoes with optimal use of resources. Due to the non-explicit solvability of the solutions, we apply an ingenious method to probe the properties of periodic solutions. Such an idea can be also applied to more general classes of hybrid switching models. Furthermore, we validate our conclusions numerically and discover some interesting phenomena. Our findings provide valuable guidance and assistance for the prevention and control of mosquito-borne diseases. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Incorporating spatial diffusion and digestion delay into an intraguild predation (IGP) model, this work demonstrates rich spatiotemporal dynamics governing biological invasions. We derive criteria for the successful invasion of the intraguild predator and identify a critical diffusion threshold that eliminates spatially heterogeneous steady states. The digestion delay induces stability switches, resulting in a finite number of stability intervals, and causing abrupt shifts in coexistence patterns as the delay crosses critical thresholds. Through steady state bifurcation analysis, we rigorously establish the emergence of spatially heterogeneous coexistence states. We further derive Turing instability conditions for Hopf-bifurcating periodic solutions in a general three-dimensional delayed diffusive system. Our results reveal multiple coexistence mechanisms, including homogeneous steady states, periodic oscillations, and complex spatiotemporal patterns, highlighting the intricate interplay between time delay and spatial heterogeneity in biological invasions. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Gene transcription is a stochastic bursting process with burst frequency and size as core parameters. While complex models capture detailed biology, their computational cost limits genome-wide applications. We propose a simple telegraph model-based framework to analyze genome-wide scRNA-seq datasets. When sample size ≥500 and burst parameter change ≥ 3 fold, inferred burst frequency- and size-dominated variations reliably proxy true regulation. Analyses across mouse cells and healthy/hypertrophic cardiomyopathy (HCM) human heart tissues revealed three conserved principles: (1) over 70% of genes with altered burst regulation exhibited burst frequency- or size-dominated regulation; HCM genes show stronger bursting featuring prolonged inactivity and intense transcription; (2) TATA-initiator synergy is lost in HCM; and (3) burst frequency-dominated genes enriched in genome stability/cell cycle/apoptosis (via TFs like Foxo4/Mcm2), while burst size-dominated ones enrich in signaling/metabolism (via TFs like Zfp322a/Ppargc1a). Their interdependent dysregulation accelerated HCM. This study establishes the simple telegraph model as a scalable framework linking transcriptional burst dynamics to cell fate and pathology.

This paper investigates the global threshold dynamics of a single-species population model subjected to unfavorable-favorable season switching and impulsive harvesting. We study the periodically switching system with impulsive harvesting on a bounded domain under Dirichlet (hostile) and Neumann (no-flux) boundary conditions. For the local (spatially homogeneous) system, we identify a threshold, & Rscr;(0), which predicts extinction when & Rscr;(0) <= 1 or the global attractiveness of a unique positive periodic solution when & Rscr;(0) > 1. We reveal a critical dependence on boundary conditions. For Dirichlet boundary, the threshold dynamics are governed by a diffusion-dependent parameter, & Rscr;(D)(0), and a diffusion-induced extinction arises: even the local system predicts persistence, sufficiently high diffusion rates during the favorable season can drive the extinction. For Neumann boundary, diffusion has no qualitative impact. There has the same threshold behavior as the local system. These results highlight the interplay between periodic environmental shifts, impulsive harvesting, and spatial diffusion for population viability. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

In this paper, we consider the following discrete periodic Ricker model \[ x_{n+1}=x_n\exp \left[r_n \left(1-\frac{x_n}{k_n}\right)\right], \quad n=0, 1, 2, \ldots , \] xn+1=xnexp[rn(1-xnkn)],n=0,1,2,& mldr;, where intrinsic growth rate $ \{ r_n \} $ {rn} and carrying capacity $ \{k_n\} $ {kn} are two given sequences of positive numbers with a common period omega. We obtain new sufficient conditions for the model to have a unique positive omega-periodic solution, which is stable and attracts all positive solutions. Our results are suitable for the case when the magnitude of the series $ \{k_n\} $ {kn} is large and partly fill a gap in the existing literature. For the special case of $ \omega =2 $ omega=2, we show the model has at most three 2-periodic solutions, and give sufficient conditions for the existence of a unique, two and three 2-periodic solutions, respectively. We also discuss and present some results regarding the minimal period of the periodic solution of the model when omega is a composite number.

To investigate the effects of seasonality and individual movement on disease transmission, we formulate a periodic SIS epidemic model with external supply governed by Fokker–Planck-type diffusion law in a spatially heterogeneous environment. A key feature of the model is the incorporation of Fokker–Planck-type diffusion to describe individual movement. We analyze the asymptotic profiles and uniform boundedness of the basic reproduction ratio R0 with respect to the dispersal rate by addressing challenges arising from periodicity and the diffusion mechanism. Under certain conditions, explicit upper bounds for the solution are derived following the comparison principle and invariant region theory. The threshold dynamics indicate that the disease-free θ-periodic solution is globally asymptotically stable as R0<1 and the system becomes uniformly persistent as R0>1. Numerical analysis demonstrates that increasing the dispersal of susceptible individuals can reduce the scale of infection. Furthermore, periodicity is shown to enhance disease persistence and induce greater complexity into the disease dynamics.

We analyze discrete-time Leslie-Gower competition models featuring Beverton-Holt survivability and interspecific mating to explore interactions between two Aedes mosquito species. By incorporating larval resource competition and asymmetric reproductive interference (satyrization), we identify conditions for equilibrium existence and local stability. We specifically examine how the mating competitiveness of Ae. albopictus and its interference with Ae. aegyptidrive competitive displacement or coexistence of the two mosquito species. Our results demonstrate that satyrization significantly alters classical competition outcomes, leading to displacement or coexistence depending on parameter regimes and initial population sizes. These findings, supported by numerical simulations, provide a robust theoretical framework for understanding how reproductive interference shapes mosquito population dynamics.

Releasing sterile mosquitoes to suppress wild mosquito population is a green and efficient method for preventing mosquito-borne diseases. In this article, we build a mosquito population suppression model with Beverton-Holt-type survival probability for offspring, and focus on the case that the release period T is smaller than the sexual lifespan T̅ of sterile mosquitoes, which is in line with the actual field releasing but has not been discussed in our previous works. Through constructive technique, we obtain that the main model admits three possibilities: (i) no periodic solution, (ii) a unique periodic solution, and (iii) exactly two periodic solutions. In addition, we analyze the stability and attractiveness of each periodic solution. Numerical simulations are provided to validate the theoretical results and to deliver practical insights for release strategy development.

. In this paper, we investigate the existence and stability of sawtooth periodic solutions of a new scalar switching system with state dependence. We find two threshold regions for the switch, denoted as DM and DM**, such that every solution will eventually converge to a constant if the threshold is located in DM, but there exists a unique globally asymptotically stable sawtooth periodic solution if it is located in DM** under suitable conditions with the aid of the Poincare mapping method. Furthermore, the non-existence of sawtooth periodic solutions is investigated through utilizing an ingenious contradiction argument which seems to be the first attempt. As an example, we apply our theory to show the existence of novel forms of sawtooth periodic solutions in a mosquito population suppression model.

In this paper, we develop a hybrid dynamical system to model mosquito population suppression incorporating both time and state-dependent switching. The time-dependent switching arises from a mismatch between the sexual lifespan of sterile mosquitoes and the sampling period, while the state-dependent switching is governed by the relation between the state of wild mosquitoes at sampling instants and the epidemiological threshold. We investigate the long-term dynamics of the hybrid system with sampling period exceeding the sexual lifespan. The wild population is shown to converge to a pseudo-equilibrium when the epidemiological threshold exceeds this equilibrium value. For the other situation, we establish sufficient conditions for the existence of a unique (pseudo)-harmonic solution and analyze its stability. Using Poincaré mapping, we further derive explicit existence criteria for subharmonic solutions and rigorously prove their global asymptotic stability. Finally, some numerical examples are provided to illustrate our theoretical findings and to deliver practical insights for release strategy development.

We study the existence and multiplicity of nontrivial homo clinic solutions for a class of periodic discrete nonlinear Schro & uml;dinger (DNLS) equations when the nonlinearities can be local superlinear or local asymptotically linear at infinity by means of the critical point theory. Principal challenges of the resulting problem entail the restriction of local growth conditions and the boundedness of Cerami sequences. We incorporate weak*-compactness for bounded sequences, unique continuation of discrete Schro & uml;dinger equations, and Lusternik-Schnirelman theory under symmetries to solve the problem. This allows us for the first time to derive a ground state and infinitely many homoclinic solutions with such assumptions, improving the relevant works in the literature. Our result implies the existence of infinitely many exponentially localized states of periodic discrete Schro & uml;dinger equations with nonlinear impurity. Our work also answers a problem of A. Pankov from the 2010's on the existence of nontrivial homo clinic solutions for periodic DNLS equations.

We study a two-species predator-prey model that incorporates predator maturation delay and the fear effect within an advective environment under general boundary conditions. First, we derive a variational expression for the principal eigenvalue associated with a general eigenvalue problem. Next, we classify the system's dynamics using basic reproduction numbers, demonstrating the global asymptotic stability of both the trivial solution and the predator-free equilibrium as well as the uniform persistence of the system and the coexistence of predator and prey. Additionally, we analyze how diffusion and advection influence the principal eigenvalues to better understand their impact on predator-prey dynamics. Our results imply that variations in the advection and diffusion rates of both predators and prey can drive multiple dynamic transitions, including successful invasions, failed invasions, and stable coexistence. Finally, by using the generalized maximum principle, we establish the uniqueness of positive steady-state solutions for a general predation system in an advective, heterogeneous environment with general boundary conditions.

In this paper, we study a periodically switching dynamical system modeling the competitive interaction between two Aedes mosquito populations under periodic releases of sterile Aedes albopictus. The system alternates between distinct regimes corresponding to the release and non-release phases, giving rise to time-dependent switching dynamics. By employing rigorous analytical techniques, we derive explicit threshold conditions on the release intensity rand the switching period T that determine the global asymptotic outcomes. These thresholds provide a complete classification of the system's long-term behavior, including extinction, coexistence, and persistence regimes. The results reveal how periodic sterile releases interact with intrinsic competition to shape the feasibility and effectiveness of population suppression strategies. (c) 2026 Published by Elsevier Inc.

We develop and analyze a mosquito population suppression delay model that incorporates survival probability during the maturation process. The model allows the trivial equilibrium to coexist with two positive equilibria and exhibits steady-state behavior including asymptotic stability, semi-stability and bistability. We analyze the subsets of basins of attraction for each stable equilibrium. Using delay as a bifurcation parameter, we examine the onset and global continuation of Hopf bifurcating periodic solutions by the global Hopf bifurcation theorem and the Bendixson criterion. Finally, some numerical examples are provided to validate the theoretical findings.

To investigate the effects of seasonality and individual movement on disease transmission, we formulate a periodic SIS epidemic model with external supply governed by Fokker-Planck-type diffusion law in a spatially heterogeneous environment. A key feature of the model is the incorporation of Fokker-Planck-type diffusion to describe individual movement. We analyze the asymptotic profiles and uniform boundedness of the basic reproduction ratio R-0 with respect to the dispersal rate by addressing challenges arising from periodicity and the diffusion mechanism. Under certain conditions, explicit upper bounds for the solution are derived following the comparison principle and invariant region theory. The threshold dynamics indicate that the disease-free theta-periodic solution is globally asymptotically stable as R-0 < 1 and the system becomes uniformly persistent as R-0 > 1. Numerical analysis demonstrates that increasing the dispersal of susceptible individuals can reduce the scale of infection. Furthermore, periodicity is shown to enhance disease persistence and induce greater complexity into the disease dynamics.

This paper studies a time-switching advection-diffusion system modelling the competition between Aedes albopictus and Aedes aegypti mosquitoes in heterogeneous environments. The switching mechanism is induced by periodic releases of sterile Ae. albopictus mosquitoes, which are active only during their sexual lifespan within each release period. By defining a minimal release amount and four critical release period thresholds, we establish the periodic dynamics of the system, providing new insights into optimal control strategies of mosquitoes. Specifically, the trivial steady state is globally asymptotically stable if sterile releases are sufficiently frequent and abundant, which ensures the eradication of both Aedes species. For less frequent sterile releases, we prove the global asymptotic stability of the two semi-trivial periodic solutions and demonstrate the existence of a coexisting periodic solution, indicating cases where mosquito control fails. Numerical simulations are presented to validate our theoretical findings.

We study a pulse-switching planar system that arises from describing the population dynamics of wild mosquitoes under the pulse-switching releases of Wolbachia-infected males. The periodic pulse switching between two systems renders the traditional qualitative method of planar systems ineffective. We develop a geometric approach to determine the maximal invariant set and the fixed points of the associated Poincare'\ map. This enables us to describe scenarios of global dynamics---extinction and bistability---in the sense of an extinction equilibrium coexisting with a periodic solution with a large amplitude and to locate the periodic solutions. Examples will be given to illustrate how our theoretical results can be used to inform the optimal design of pulse-releasing strategies.