Non-binding communication is common in daily life and crucial for fostering cooperation, even though it has no direct payoff consequences. However, despite robust empirical evidence, its evolutionary basis remains poorly understood. Here, we develop a game-theoretic model in which individuals can signal an intention to cooperate before playing a Donation game. Strategies differ in how they respond to these signals, ranging from unconditional to conditional types, with the latter incurring a cognitive cost for deliberation. Through evolutionary analysis, we show that non-binding communication alone cannot sustain cooperation in well-mixed, anonymous populations, consistent with empirical observations. In contrast, structured populations support the emergence of cooperation, with conditional cooperators acting as catalysts that protect unconditional cooperators through context-dependent patterns of cyclic dominance. These findings offer an evolutionary explanation for how non-binding communication promotes cooperation and provide a modelling framework for exploring its effects in diverse social settings.

A social norm defines what is good and what is bad in social contexts, as well as what to do based on such assessments. A stable social norm should be maintained against errors committed by its players. In addition, individuals may have different probabilities of errors in following the norm, and a social norm would be unstable if it benefited those who do not follow the norm carefully. In this work, we show that Simple Standing, which has been known to resist errors and mutants successfully, actually exhibits threshold behavior. That is, in a population of individuals playing the donation game according to Simple Standing, the residents can suppress the invasion of mutants with higher error proneness only if the residents' own error proneness is sufficiently low. Otherwise, the population will be invaded by mutants that commit assessment errors more frequently, and a series of such invasions will eventually undermine the existing social norm. This study suggests that the stability analysis of a social norm may have a different picture if the probability of error itself is regarded as an individual attribute.

Varroa destructor is a significant European honeybee pest, impacting agricultural industries globally. Since arriving in 2022, Australia faces the possibility that Varroa will become established in European honeybee colonies nationally. Australia initially pursued a strategy of testing and subsequently eliminating hives infested with Varroa. These management efforts raise interesting questions about the interplay between hive testing and elimination, and the spread of Varroa between hives. This study uses mathematical modelling to investigate how combined hive testing and elimination strategies impact the spread of Varroa through a network of European honeybee hives. We develop a model of both within-hive reproduction of Varroa and hive testing, and between-hive movement of Varroa on a network of hives. This model is used to assess the impact of various testing and hive elimination strategies on the total number of hives eliminated on the network of hives. Each model simulation starts with a single infested hive, and from this we observed one of two dynamics: either the infestation is caught before spreading, or Varroa spreads extensively through the network before being caught by testing. Within our model we implement two common hive testing methods - sugar shake and alcohol testing. A shared limitation of these testing methods is that they can only detect mites in a specific stage of their lifecycle. As such, testing is not only dependent on how many Varroa mites are in a hive, but also on what lifecycle stage the mites are in at the time of testing. By varying testing and movement parameters, we see that this testing limitation greatly impacts the number of hives eliminated in various scenarios. Furthermore, testing earlier, or testing more frequently, does not guarantee a smaller invasion. Our model results suggest irregular testing schedules, e.g. testing multiple times in close succession rather than just once in a given timeframe, may help overcome the limitations of common hive testing strategies.

Habitat fragmentation is a leading cause of biodiversity loss, and efforts to enhance connectivity through, for example, biological corridors are a common conservation strategy to mitigate it. However, understanding the effects of dispersal variation on the total biomass of spatially structured populations is still far from being well understood. For the simplest situation, i.e., a population occupying a habitat divided into two patches, recent studies have shown that there are only four possible response scenarios to increased connectivity in discrete- and continuous-time models under Beverton-Holt and logistic local dynamics, respectively. This paper explores whether the number of patches in a metapopulation influences the number of response scenarios to increased dispersal. We will show that for given local dynamics the number of possible response scenarios significantly increases when the number of patches increases from two to three. Moreover, the paper revisits the problem of how network topology affects total biomass dynamics for low dispersal rates. We will show that the previous claim that bidirectional connectivity always increases biomass at low dispersal rates when connecting sources is false. Indeed, we will prove that transiting from a chain topology to a ring topology can either increase or decrease the total biomass for low dispersal rates if one considers more realistic production functions or if the probability of using a concrete path is not the same in the whole metapopulation.

Spatial heterogeneity and population migration may affect transmission threshold and the asymptotic behavior of epidemic transmission near the steady state. To investigate this issue, an epidemic transmission model with nonlinear natural growth mechanism and linear migration mechanism based on multi-patch structure is established. First, we study the findings related to the equilibrium state of the system and the transmission threshold, proving the uniqueness and the existence of epidemic-free equilibrium points, the existence of positive equilibrium points under certain conditions and the non-existence of mixed equilibrium points. Meanwhile, we discuss the asymptotic behavior of various types of equilibrium points and define the global basic reproduction number and the local basic reproduction number, demonstrating some of their unequal relationships. Further, we also consider the impact of the blocking mechanism on the patch model, illustrating that the epidemic disappears or persists in single patch under certain conditions. Finally, we carry out the numerical simulation analysis of our system. The results suggest that the epidemic may form a certain oscillatory pattern in space and there are multiple positive equilibrium points for the system. At the same time, the blocking mechanism may lead to different types of equilibrium states in different patches, but it is not effective in reducing the total number of infected individuals and the convergence time of the system.

Direct reciprocity is a fundamental mechanism for sustaining cooperation in repeated interactions, where individuals adjust their behavior based on past experiences. Most previous models have focused on the prisoner's dilemma, in which individuals face a strict choice between full cooperation and complete defection. However, this dichotomy oversimplifies the complexity of real-world reciprocal interactions. To address this, we introduce additional actions between these extremes, thereby increasing action diversity. Our analysis demonstrates that a broader range of available actions fosters cooperation more effectively than a binary choice. Through evolutionary analysis, we identify which types of intermediate actions promote cooperation. Moreover, equilibrium analysis establishes the theoretical conditions underlying this effect. While the increased computational complexity makes it infeasible to simulate scenarios with an arbitrarily large number of actions, our theoretical analysis remains applicable to settings with more actions, offering broader insights into the role of action diversity in promoting cooperation. These findings deepen our understanding of direct reciprocity and highlight the importance of action diversity in shaping cooperative behavior.

Ebola and Marburg viruses are highly pathogenic filoviruses that cause severe hemorrhagic fever in humans, with case fatality rates reaching approximately 50 %. These viruses pose significant public health challenges owing to their potential for large-scale outbreaks. A key step in their infection process is the interaction between the Niemann-Pick C1 (NPC1) protein on host cells and the viral glycoprotein (GP), which is responsible for viral entry into cells. Genetic variations in NPC1 caused by single nucleotide polymorphisms (SNPs) can lead to amino acid substitutions, potentially altering the efficiency of viral entry. To better understand this process, we developed an agent-based model (ABM) to simulate viral plaque growth with spatial resolution beyond traditional models. By applying this model, we quantified how naturally occurring SNPs at GP-binding interface of NPC1, such as D508N, P424A, and S425L, reduced entry efficiency of both Ebola and Marburg viruses. Notably, the P424A substitution led to a 53 % reduction in Ebola virus entry efficiency compared to the wild-type. Our findings highlight the potential of computational modeling to uncover the impact of genetic variations on viral infections and provide insights that may inform therapeutic strategies against these deadly viruses.

The dynamic interplay between tumors and immune system is pivotal to the progression of breast cancer. To systematically investigate how interactions between tumor cells and immune cells shape breast cancer evolution, we developed a mathematical model that incorporates tumor cells, dendritic cells (DCs), natural killer (NK) cells, regulatory T cells (Tregs) and CD8+ T cells. We first established analytical conditions for the local stability of the tumor-free equilibrium, identifying key constraints on tumor growth imposed by immune activity. The existence of a positive equilibrium solution further suggests the potential coexistence of tumor and immune cells. Numerical simulations demonstrate that effective tumor control is achieved under a high baseline level of CD8+ T cell precursors coupled with a low level of regulatory T cell precursors. These results highlight the important role of balancing immunostimulatory and immunosuppressive forces within the tumor microenvironment. Through bifurcation analysis, we identified regimes of bistability in which both high-tumor and low-tumor equilibria coexist with dynamic features that may underlie divergent clinical outcomes and present a critical challenge for clinical therapeutic intervention. Moreover, simulations of tumor-immune dynamics in virtual cohorts reveal that tumor control hinges on CD8+ T cell infiltration, whereas regulatory T cell abundance is a potent predictor of immune escape. Finally, we formulated an optimal control framework to design adaptive CD8+ T cell injection protocols. Numerical solutions demonstrate that such optimized strategies achieve superior tumor reduction compared with constant dosing, despite using the same total injection dose of CD8+ T cells and identical treatment intervals. Collectively, our findings provide a mechanistic understanding of breast cancer progression and establish a theoretical foundation for developing personalized therapeutic strategies to optimize clinical outcomes.

White adipose tissue, composed of adipocyte cells, primarily stores energy as lipid droplets. The size of adipocytes varies significantly within the tissue according to the amount of stored lipids. A striking observation is that the adipocyte size distribution is bimodal, and thus, this tissue is lacking a characteristic size. We propose a novel dynamical model, based on a partial differential equation, to represent the adipocyte size distribution. The model assumes continuous adipocyte growth, with a velocity dependent on cell radius and extracellular lipid availability, together with constant rates of cell recruitment and death. We prove the existence and local stability of a unique stationary solution for a broad range of growth velocity functions. Choosing a parcimonious formulation, we show that only three parameters are enough to describe adipocyte size distributions measurements in rats. These parameters are robustly estimated through approximate Bayesian computation, and the model demonstrates excellent agreement with experimental data. This mechanistic, three-parameter framework offers a new and interpretable approach to characterizing adipocyte size distributions.

Methanol poisoning is an infrequent but immensely dangerous intoxication, causing severe metabolic disturbances, neurological dysfunction, and even death, if not treated timely and properly. In this article, we formulate a mathematical model based on the chemical kinetics reaction, to analyse the effect of co-administration of the antidote ethanol and folinic acid for the treatment of methanol toxicity. The maximum concentration level of formic acid has been identified, and through a one-dimensional impulsive system, we determined the maximum dosing interval of folinic acid. Under appropriate assumptions we have demonstrated the existence and stability of the equilibrium-like periodic orbit of our system with impulsive administration of folinic acid and ethanol. The dynamical changes of toxic metabolites are illustrated numerically for different doses and dosing intervals. We performed a sensitivity analysis to identify the key parameters affecting formic acid concentration during treatment. Model results were validated by comparing them with clinical and experimental data on methanol half-life during ethanol therapy and formic acid clearance under folinic acid treatment. Based on our detailed analytical and numerical analysis, we recommend an effective dosing regimen of folinic acid and ethanol to detoxify the human body and clearly identify the conditions beyond which hemodialysis becomes essential. We verified all of our analytical outcomes through numerical simulation.

Cardiac cells communicate electrically to coordinate heart contractions and pump blood. Gap junctions in the intercalated discs (ID) between myocytes form low-resistance pathways that facilitate electrical propagation. Traditionally, gap junctional coupling is considered the primary mechanism for cell communication, but experimental studies show that conduction can persist even with impaired gap junctions. For example, in gap junction-deficient rats, the heart still shows slow, discontinuous signal propagation, suggesting the existence of other communication mechanisms. One such mechanism is ephaptic coupling (EpC), an electrical field effect in the ID that maintains conduction even in the absence of gap junctions. EpC has been explored experimentally and numerically, especially in altered ID under normal and diseased conditions. However, a lack of direct evidence emphasizes the need to study its physiological role in the heart. Some research indicates that EpC can increase conduction velocity (CV) and reduce conduction failure, but its effects on cardiac arrhythmias are not well understood. Our study focuses on reentry arrhythmia, where rapid, irregular heartbeats can lead to cardiac arrest. Previous modeling work suggests that strong EpC can terminate reentry in ischemic hearts, though the mechanism remains unclear. We aim to investigate the mechanisms underlying reentry termination across different levels of EpC and gap junctional coupling using a two-dimensional discrete bidomain model with EpC. Our results identify two mechanisms: (1) Strong EpC terminates reentry through self-attenuation, driven by inactivation of fast sodium currents and (2) moderate EpC terminates reentry through self-collision, influenced by increased CV and anisotropy. A boundary where termination does not occur is also observed.

Coordinated longitudinal queue behavior in biological groups, such as migratory bird flocks, remains underexplored in classical collective motion models that focus on metric-based interactions and synchronous dynamics. This study utilizes a modified self-propelled particle model incorporating topological interactions, gliding asynchrony, and limited view angle to investigate the mechanisms driving longitudinal queue formation. Simulations reveal that interacting with only two topological neighbors is critical for stable queue emergence, with an optimal view angle range of [200°, 270°] balancing frontward tracking and lateral collision avoidance. Gliding asynchrony enhances queue formation efficiency by reducing neighbor interaction frequency, leading to higher success rates and lower interaction complexity compared to synchronous or random update mechanisms. Topological interaction networks exhibit high connectivity and stability, fundamentally supporting queue maintenance, while metric-based or Voronoi interactions fail to produce linear order. The study highlights the interplay of limited sensory perception, low neighbor connectivity, and asynchronous dynamics in self-organized migration queues, providing a theoretical guidance for understanding animal collective behavior and guiding robotic swarm design.

An increasingly important goal in the design of antimicrobial treatment regimens is to minimise the probability of resistance evolving, without harming individual patients' outcomes. A key characteristic to consider when choosing an antibiotic for treatment is its mode of action: bacteriostatic (growth-inhibiting) or bactericidal (mortality-inducing). We present a theoretical model comparing the efficacy of bacteriostatic, bactericidal, and intermediate drugs at preventing the evolutionary rescue of an initially susceptible bacterial population. We find that, all else equal, in resource-abundant environments, bacteriostatic drugs are best, as they constrain cell divisions and thus allow fewer resistance mutations to occur. This contrasts with the prevailing assumption that bactericidal drugs are best as they actively kill cells. When multiple drugs are employed, using one bacteriostatic and one bactericidal drug is usually optimal, because the cell division rate cannot fall below zero, so there are diminishing returns to bacteriostatic activity from two drugs. Severe resource constraints mean that growth rates are already low, and thus there is less benefit to bacteriostatic drugs further limiting growth, so bactericidal drugs are favoured. If these findings are empirically verified in the laboratory and in vivo, they could significantly guide clinical practice.

The goal of our study was to establish how a specific part of the bone Gene Regulatory Network (GRN) controls mineralization in response to stiffness. We hypothesized that a system of differential equations model stiffness-sensitive gene regulation in human mesenchymal stem cells through the epistatic genetic interactions between stiffness (e.g. WNT-β catenin pathway) and five of the main transcription factors and bone proteins (e.g. RUNX2, BSP, OSX, OC, and OPN). To test this hypothesis, we (i) performed in-vitro experiments culturing bone cells on different stiffness, (i) adapted our previously published model from being continuously time-dependent to continuously stiffness-sensitive, and (iii) simulated protein production in function of stiffness and other protein production from the best estimate of parameters coming from the experimental work. Our experimental findings reveal a non-parametric relationship between stiffness and RUNX2 production, with no discernible linear trends for other proteins. Modeling results demonstrate that continuous variations in stiffness enable simulation of bone GRN gene expression, fitting our novel experimental dataset. Specifically, our computational results indicate that OPN production peaks at low stiffness (8 kPa), while RUNX2, OSX, and OC achieve maximum production at higher stiffness levels (64 kPa). This alignment underscores the model's capacity to replicate experimental data accurately. Additionally, our approach predicts that WNT-β-catenin activation serves as an enhancer for OPN and BSP production. The model also highlights a negative feedback-like interaction between OC and BSP production. Stiffness variations were shown to have a significant impact on OC and BSP production and a moderate effect on OPN production. By employing a stiffness-sensitive gene regulation model, we provide insights into one of the mineralization patterns through the prediction of bone protein expression dynamics.

Despite the widespread use of deterministic models in understanding and controlling epidemics, they are often criticized for their inability to provide timely practical solutions during rapid spread. Similarly, conventional stochastic and statistical models also have limitations in providing time-sensitive solutions. These models are useful for implementing policy measures when there is enough time to make changes. In this article, we propose a novel approach to address these limitations by introducing a graphical network model with time-sensitive data blending to enhance deterministic epidemic models like the SIR model. This innovative approach could be valuable for rapidly spreading epidemics, providing timely model-based solutions to control their spread. For the first time, this article introduces higher-dimensional transmission rate functions in the literature and methods to obtain such functions. AMS MSC 2020 classifications: 92D30; 62P10; 65T60.

Epidemiological models can inform policymaking on disease control strategies, and these models often rely on sampled contact networks. The Random Walk (RW) sampling algorithm, commonly used for network sampling, produces size-biased samples that over-represent highly connected individuals, leading to biased estimates of disease spread. The Metropolis-Hastings Random Walk (MHRW) addresses this by providing samples representative of the underlying network's connectivity distribution. We compare MHRW and RW in reducing size bias across four network types: Erdös-Rényi (ER), Small-world (SW), Negative-binomial (NB), and Scale-free (SF). We simulate disease spread using a stochastic Susceptible-Infected-Recovered (SIR) framework. RW tends to overestimate infections (by 25 % in ER, SW, NB) and secondary infections (by 25 % in ER, SW and 80 % in NB), and underestimate time-to-infection in NB networks. MHRW reduces the size bias, except on SF networks, where both algorithms provide non-representative samples and highly variable estimates. We find that RW is appropriate for fast-spreading, high-mortality epidemics in homogeneous or moderately random networks (ER, SW). In contrast, MHRW is better suited for slower and low-severity epidemics and can be effective in both homogeneous and heterogeneous networks (ER, SW, NB). However, MHRW is computationally expensive and less accurate when duplicate nodes are removed. We also analyse real-world data from cattle movement and human contact networks; MHRW generates disease spread estimates closer to the underlying network than RW. Our findings guide the selection of sampling algorithms based on network structure and epidemic characteristics, enhancing the reliability of disease modelling for policymaking.

Electroporation-based therapies such as electrochemotherapy (ECT) hold a great promise for improving cancer treatments. While highly effective for superficial tumours, its application for deep-seated malignancies is challenged by complex microstructural properties, and current models often lack a multiscale theoretical framework to capture those phenomena. Here we develop and solve a novel system of coupled partial differential equations of Darcy-Laplace type obtained by applying the asymptotic homogenisation technique. We study the tumour response stimulated by an electric field. We derive effective macroscale equations for the pressure, velocity, and electric potential, whilst incorporating both hydraulic and electric microscale tissue heterogeneities. Our coupled multiscale approach bridges the gap between the tumour microstructure and macroscale dynamics, offering a more comprehensive understanding of how tumour size, morphology, and hydraulic-electrical interactions influence interstitial flow. We present a parametric analysis of the hydraulic conductivity tensor and macroscale numerical simulation results for pressure and velocity fields, highlighting the role of the electric field in modulating fluid flow. Our findings provide meaningful insights towards advancing ECT protocols.

The current standard treatment for HIV-1 infection is antiretroviral therapy, which effectively suppresses viral replication but requires a lifelong drug regimen. An alternative treatment approach is a single injection of a modified version of the HIV-1 virus, termed a therapeutic interfering particle (TIP), that lacks replication machinery and suppresses the wild-type virus by competing for viral proteins. Here, we derive a novel ordinary differential equation model of TIP dynamics. We confirm results from previous models that TIPs can reduce viral load when doubly infected cells produce at least as many virus particles as singly infected cells. By deriving the basic reproduction number R of a TIP, we predict that concurrent antiretroviral therapy should make it more difficult for a TIP to persist in a host. Adding an immune response to our model reveals that even a moderate immune response against virally infected cells drastically decreases the range of parameter values for which therapy is effective. Together, these results show that the success of TIPs depend on the properties of the wild-type virus and even more strongly on the immune response, which makes it hard to predict therapeutic success.

Naomi is a spatial evidence synthesis model used to produce district-level HIV epidemic indicators in sub-Saharan Africa. Multiple outcomes of policy interest, including HIV prevalence, HIV incidence, and antiretroviral therapy treatment coverage are jointly modelled using both household survey data and routinely reported health system data. The model is provided as a tool for countries to input their data to and generate estimates with during a yearly process supported by UNAIDS. Previously, inference has been conducted using empirical Bayes and a Gaussian approximation, implemented via the TMBR package. We propose a new inference method based on an extension of adaptive Gauss-Hermite quadrature to deal with more than 20 hyperparameters. Using data from Malawi, our method improves the accuracy of inferences for model parameters, while being substantially faster to run than Hamiltonian Monte Carlo with the No-U-Turn sampler. Our implementation leverages the existing TMBC++ template for the model's log-posterior, and is compatible with any model with such a template.

Tuberculosis (TB) remains a significant global health threat, particularly in the regions with diverse age-specific transmission patterns and increasing drug resistance. To address these challenges, this study establishes a dual-strain model that incorporates both drug-resistant and drug-sensitive strains to investigate how these strains contribute to the dynamics of TB transmission. By integrating age heterogeneity, social interactions, and seasonal variations, the model offers a detailed depiction of TB transmission process, highlighting its inherent complexity across various population groups. We derive the basic reproduction number of the model as the maximum of the two reproduction numbers: one for the drug-resistant strain (R) and one for the drug-sensitive strain (R). It is found that the disease-free periodic equilibrium of the system is globally asymptotically stable when R=max(R,R)<1, in the absence of reinfection. We further explore the competitive dynamics of drug-resistant and drug-sensitive strains under R>1>R and R>1>R. Using a Markov Chain Monte Carlo (MCMC) algorithm, the model is calibrated with monthly TB infection data from mainland China, enabling the reconstruction of TB transmission dynamics across eight age-specific groups. The study reveals that drug-sensitive tuberculosis strains exhibit more prominent transmission characteristics compared to drug-resistant strains. Moreover, increased vaccination coverage significantly reduces TB prevalence, particularly in younger populations, while reducing contact intensity effectively suppresses TB across all age groups. These findings highlight the role of combining age-structured modeling, strain dynamics, and behavioral interventions, offering implications for the targeted TB control strategies.

Reproductive interference (RI) includes any negative effect on reproductive success of females that is induced by interspecific sexual interactions. Although previous population dynamic models of RI have focused on population-level processes (e.g., changes in population size), individual-level processes (e.g., search and courtship by males and subsequent choice by females) have been largely overlooked. In this study, we constructed a discrete-time population dynamic model comprising two species, assuming iterative courtship and mating within each reproductive time period (i.e., individual-level process) and subsequent population dynamics (i.e., population-level process). We assumed that if males (or females) have wide acceptance range to their counterparts, correct courtship (or mating) to conspecifics and incorrect courtship to heterospecifics would increase simultaneously. We also assumed that two species have different demographics (species 1 with higher reproduction and mortality, species 2 with lower reproduction and mortality). We showed that intermediate acceptance range of females mitigated the negative effect of courtship from heterospecific males on mating success. However, the initially more abundant species 1 can be outcompeted by the initially less abundant species 2. This is because the net negative effect of losing mating opportunities due to RI was greater for species 1 with higher mortality than for species 2 with lower mortality. Overall, the results of reproductive success, which are derived only from individual-level processes, are not always consistent with the demographic consequences, which are derived from both individual- and population-level processes. We propose that analyzing the RI system by considering both individual- and population-level processes is necessary.