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Synchronization is one of the most striking instances of collective behavior, occurring in many natural phenomena. For example, in some ant species, ants are inactive within the nest most of the time, but their bursts of activity are highly synchronized and involve the entire nest population. Here we revisit a simulation model that generates this synchronized rhythmic activity through autocatalytic behavior, i.e., active ants can activate inactive ants, followed by a period of rest. We derive a set of delay differential equations that provide an accurate description of the simulations for large ant colonies. Analysis of the fixed-point solutions, complemented by numerical integration of the equations, indicates the existence of stable limit-cycle solutions when the rest period is greater than a threshold and the event of spontaneous activation of inactive ants is very unlikely, so that most of the arousal of ants is done by active ants. Furthermore, we argue that the persistent oscillations observed in the simulations for colonies of finite size are due to resonant amplification of demographic noise., Competing Interests: Declaration of competing interest None, (Copyright © 2024 Elsevier Inc. All rights reserved.)

In this paper, we introduce a stochastic two-strain epidemic model driven by Lévy noise describing the interaction between four compartments; susceptible, infected individuals by the first strain, infected ones by the second strain and the recovered individuals. The forces of infection, for both strains, are represented by saturated incidence rates. Our study begins with the investigation of unique global solution of the suggested mathematical model. Then, it moves to the determination of sufficient conditions of extinction and persistence in mean of the two-strain disease. In order to illustrate the theoretical findings, we give some numerical simulations., Competing Interests: Declaration of competing interest The authors declare no conflict of interest regarding the publication of this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

In epidemiology, realistic disease dynamics often require Susceptible-Exposed-Infected-Recovered (SEIR)-like models because they account for incubation periods before individuals become infectious. However, for the sake of analytical tractability, simpler Susceptible-Infected-Recovered (SIR) models are commonly used, despite their lack of biological realism. Bridging these models is crucial for accurately estimating parameters and fitting models to observed data, particularly in population-level studies of infectious diseases. This paper investigates stochastic versions of the SEIR and SIR frameworks and demonstrates that the SEIR model can be effectively approximated by a SIR model with time-dependent infection and recovery rates. The validity of this approximation is supported by the derivation of a large-population Functional Law of Large Numbers (FLLN) limit and a finite-population concentration inequality. To apply this approximation in practice, the paper introduces a parameter inference methodology based on the Dynamic Survival Analysis (DSA) survival analysis framework. This method enables the fitting of the SIR model to data simulated from the more complex SEIR dynamics, as illustrated through simulated experiments., Competing Interests: Declaration of competing interest The authors declare no conflicts of interest., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)

The dynamics of locally interacting particles that are distributed in space give rise to a multitude of complex behaviours. However the simulation of reaction-diffusion processes which model such systems is highly computationally expensive, the cost increasing rapidly with the size of space. Here, we devise a graph neural network based approach that uses cheap Monte Carlo simulations of reaction-diffusion processes in a small space to cast predictions of the dynamics of the same processes in a much larger and complex space, including spaces modelled by networks with heterogeneous topology. By applying the method to two biological examples, we show that it leads to accurate results in a small fraction of the computation time of standard stochastic simulation methods. The scalability and accuracy of the method suggest it is a promising approach for studying reaction-diffusion processes in complex spatial domains such as those modelling biochemical reactions, population evolution and epidemic spreading., Competing Interests: Declaration of competing interest The authors declare no conflict of interests., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

We consider compartmental models of communicable disease with uncertain contact rates. Stochastic fluctuations are often added to the contact rate to account for uncertainties. White noise, which is the typical choice for the fluctuations, leads to significant underestimation of the disease severity. Here, starting from reasonable assumptions on the social behavior of individuals, we model the contacts as a Markov process which takes into account the temporal correlations present in human social activities. Consequently, we show that the mean-reverting Ornstein-Uhlenbeck (OU) process is the correct model for the stochastic contact rate. We demonstrate the implication of our model on two examples: a Susceptibles-Infected-Susceptibles (SIS) model and a Susceptibles-Exposed-Infected-Removed (SEIR) model of the COVID-19 pandemic and compare the results to the available US data from the Johns Hopkins University database. In particular, we observe that both compartmental models with white noise uncertainties undergo transitions that lead to the systematic underestimation of the spread of the disease. In contrast, modeling the contact rate with the OU process significantly hinders such unrealistic noise-induced transitions. For the SIS model, we derive its stationary probability density analytically, for both white and correlated noise. This allows us to give a complete description of the model's asymptotic behavior as a function of its bifurcation parameters, i.e., the basic reproduction number, noise intensity, and correlation time. For the SEIR model, where the probability density is not available in closed form, we study the transitions using Monte Carlo simulations. Our modeling approach can be used to quantify uncertain parameters in a broad range of biological systems., Competing Interests: Declaration of competing interest The author declare that they do not have any competing interests., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Integrated Pest Management (IPM) poses a challenge in determining the optimal timing of pesticide sprays to ensure that pest populations remain below the Economic Injury Level (EIL), due to the long-term residual effects of many pesticides and the delayed responses of pest populations to pesticide sprays. To address this issue, a specific pesticide kill-rate function is incorporated into a deterministic exponential growth model and a subsequent stochastic model. The findings suggest the existence of an optimal pesticide spraying cycle that can periodically control pests below the EIL. The results regarding stochasticity indicate that random fluctuations promote pest extinction and ensure that the pest population, under the optimal cycle, does not exceed the EIL on average, even with a finite number of IPM strategies. All those confirm that the modeling approach can accurately reveal the intrinsic relationship between the two key indicators Economic Threshold and EIL in the IPM strategy, and further realize the precise characterization of the residual effect and delayed response of pesticide application., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions. We use these to study the phase diagram of the stochastic model; in particular we derive parametric conditions determining three types of transitions in the properties of mRNA fluctuations: from sub-Poissonian to super-Poissonian noise, from high noise in the nucleus to high noise in the cytoplasm, and from a monotonic increase to a monotonic decrease of the Fano factor with the number of processing stages. In contrast, protein fluctuations are always super-Poissonian and show weak dependence on the number of mRNA processing stages. Our results delineate the region of parameter space where conventional models give qualitatively incorrect results and provide insight into how the number of processing stages, e.g. the number of rate-limiting steps in initiation, splicing and mRNA degradation, shape stochastic gene expression by modulation of molecular memory., Competing Interests: Declaration of competing interest The authors declare no conflict of interests., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Antimicrobial heteroresistance refers to the presence of different subpopulations with heterogeneous antimicrobial responses within the same bacterial isolate, so they show reduced susceptibility compared with the main population. Though it is widely accepted that heteroresistance can play a crucial role in the outcome of antimicrobial treatments, predictive Antimicrobial Resistance (AMR) models accounting for bacterial heteroresistance are still scarce and need to be refined as the techniques to measure heteroresistance become standardised and consistent conclusions are drawn from data. In this work, we propose a multivariate Birth-Death (BD) model of bacterial heteroresistance and analyse its properties in detail. Stochasticity in the population dynamics is considered since heteroresistance is often characterised by low initial frequencies of the less susceptible subpopulations, those mediating AMR transmission and potentially leading to treatment failure. We also discuss the utility of the heteroresistance model for practical applications and calibration under realistic conditions, demonstrating that it is possible to infer the model parameters and heteroresistance distribution from time-kill data, i.e., by measuring total cell counts alone and without performing any heteroresistance test., Competing Interests: Declaration of competing interest The authors have declared no conflict of interest., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

Investigating disease progression, transmission of infection and impacts of Multidrug Therapy (MDT) to inhibit demyelination in leprosy involves a certain amount of difficulty in terms of the in-built uncertain complicated and complex intracellular cell dynamical interactions. To tackle this scenario and to elucidate a more realistic, rationalistic approach of examining the infection mechanism and associated drug therapeutic interventions, we propose a four-dimensional ordinary differential equation-based model. Stochastic processes has been employed on this deterministic system by formulating the Kolmogorov forward equation introducing a transition state and the quasi-stationary distribution, exact distribution analysis have been investigated which allow us to estimate an expected time to extinction of the infected Schwann cells into the human body more prominently. Additionally, to explore the impact of uncertainty in the key intracellular factors, the stochastic system is investigated incorporating random perturbations and environmental noises in the disease dissemination, proliferation and reinfection rates. Rigorous numerical simulations validating the analytical outcomes provide us significant novel insights on the progression of leprosy and unravelling the existing major treatment complexities. Analytical experiments along with the simulations utilizing Monte-Carlo method and Euler-Maruyama scheme involving stochasticity predicts that the bacterial density is underestimated due to the recurrence of infection and suggests that maintaining a drug-efficacy rate in the range 0.6-0.8 would be substantially efficacious in eradicating leprosy., Competing Interests: Declaration of competing interest The authors declare no conflict of interest at all., (Copyright © 2024 Elsevier Inc. All rights reserved.)

We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations., Competing Interests: Declaration of competing interest Declarations of interest: none, (Copyright © 2024 Elsevier Inc. All rights reserved.)

Antibiotics Time Machine is an important problem to understand antibiotic resistance and how it can be reversed. Mathematically, it can be modeled as follows: Consider a set of genotypes, each of which contain a set of mutated and unmutated genes. Suppose that a set of growth rate measurements of each genotype under a set of antibiotics is given. The transition probabilities of a 'realization' of a Markov chain associated with each arc under each antibiotic are computable via a predefined function given the growth rate realizations. The aim is to maximize the expected probability of reaching to the genotype with all unmutated genes given the initial genotype in a predetermined number of transitions, considering the following two sources of uncertainties: (i) the randomness in growth rates, (ii) the randomness in transition probabilities, which are functions of growth rates. We develop stochastic mixed-integer linear programming and dynamic programming approaches to solve static and dynamic versions of the Antibiotics Time Machine Problem under the aforementioned uncertainties. We adapt a Sample Average Approximation approach that exploits the special structure of the problem and provide accurate solutions that perform very well in an out-of-sample analysis., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

The collective foraging behavior of ant colonies is a central focus in behavioral ecology. This paper enhances the classical model of foraging dynamics in harvester ant colonies by introducing a nonlinear recruitment rate and considering environmental variability. Initially, we analyze the existence and stability of steady states in the deterministic model. The results suggest that an increase in mean recruitment time can reduce the foraging threshold, leading to both forward and backward bifurcations. Furthermore, both average recruitment time and the interference intensity of recruiters impact the number of workers in each subgroup. Subsequently, we conduct an analysis of the long-term and transient dynamics of collective foraging in random environments, providing sufficient conditions for the colony to sustain foraging activity. The findings emphasize the scene-dependent impact of environmental stochasticity on foraging dynamics. When ant colonies deterministically cease foraging, environmental stochasticity may unexpectedly prolong the foraging state. Conversely, when colonies deterministically persist in foraging, environmental stochasticity may disrupt this continuity. Additionally, the effect of environmental stochasticity on foraging status varies with the initial worker size. Sizes near the boundary of the basin of attraction between non-foraging and foraging states exhibit greater sensitivity to environmental stochasticity, and sufficiently large stochasticity can impact foraging dynamics across a broader range of initial worker sizes. These findings underscore the intricate interplay between intrinsic factors (e.g., recruitment efficiency and interference intensity) and extrinsic factors (e.g., environmental stochasticity) in shaping the collective foraging dynamics of ant colonies., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Inc. All rights reserved.)

A fundamental question of cell biology is how cells control the number of organelles. The processes of organelle biogenesis, namely de novo synthesis, fission, fusion, and decay, are inherently stochastic, producing cell-to-cell variability in organelle abundance. In addition, experiments suggest that the synthesis of some organelles can be bursty. We thus ask how bursty synthesis impacts intracellular organelle number distribution. We develop an organelle biogenesis model with bursty de novo synthesis by considering geometrically distributed burst sizes. We analytically solve the model in biologically relevant limits and provide exact expressions for the steady-state organelle number distributions and their means and variances. We also present approximate solutions for the whole model, complementing with exact stochastic simulations. We show that bursts generally increase the noise in organelle numbers, producing distinct signatures in noise profiles depending on different mechanisms of organelle biogenesis. We also find different shapes of organelle number distributions, including bimodal distributions in some parameter regimes. Notably, bursty synthesis broadens the parameter regime of observing bimodality compared to the 'non-bursty' case. Together, our framework utilizes number fluctuations to elucidate the role of bursty synthesis in producing organelle number heterogeneity in cells., Competing Interests: Declaration of competing interest The authors declare no competing interests., (Copyright © 2024 Elsevier Inc. All rights reserved.)

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the spatial-stochastic particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios., Competing Interests: Declaration of competing interest We hereby declare no conflict of interest., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy., Competing Interests: Declaration of competing interest There is non-financial interest in this research., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Engaging in smoking not only leads to substantial health risks but also imposes considerable financial burdens. To deepen our understanding of the mechanisms behind smoking transmission and to address the tobacco epidemic, we examined a five-dimensional smoking epidemic model that accounts for different degrees of smoking under both deterministic and stochastic conditions. In the deterministic case, we determine the basic reproduction number, analyze the stability of equilibria with and without smoking, and investigate the existence of saddle-node bifurcation. Our analysis reveals that the basic reproduction number cannot completely determine the existence of smoking, and the model possesses bistability, indicating its dynamic is susceptible to interference from environmental noises. In the stochastic case, we establish sufficient conditions for the ergodic stationary distribution and the elimination of smokers by constructing appropriate Lyapunov functions. Numerical simulations suggest that the effects of inevitable random fluctuations in the natural environment on controlling the smoking epidemic may be beneficial, harmful, or negligible, which are closely related to the noise intensities, initial smoking population sizes, and the effective exposure rate of smoking transmission (β). Given the uncontrollable nature of environmental random effects, effective smoking control strategies can be achieved by: (1) accurate monitoring of initial smoking population sizes, and (2) implementing effective measures to reduce β. Therefore, it is both effective and feasible to implement a complete set of strong MPOWER measures to control smoking prevalence., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

For infections that become endemic in a population, the process may appear stable over a long time scale, but stochastic fluctuations can lead to eventual disease extinction. We consider the effects of model parameters and of population heterogeneities upon the expected time to extinction for host-vector disease systems. We find that non-homogeneous host selection by vectors increases persistence times relative to the homogeneous case, and that the effect becomes even more marked when there are strong associations between particular groups of vectors and hosts. Heterogeneity in vector lifespans, in contrast, is found to decrease persistence times relative to the homogeneous case. Neither the basic reproduction number R 0 , nor the endemic prevalence level in the corresponding deterministic model, is found to be sufficient to predict (for a given population size) time to extinction. The endemic level, in particular, proves a very unreliable guide to the duration of long-term persistence., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 The Author(s). Published by Elsevier Inc. All rights reserved.)

Compartmentalized biochemical reactions are a ubiquitous building block of biological systems. The interplay between chemical and compartmental dynamics can drive rich and complex dynamical behaviors that are difficult to analyze mathematically - especially in the presence of stochasticity. We have recently proposed an effective moment equation approach to study the statistical properties of compartmentalized biochemical systems. So far, however, this approach is limited to polynomial rate laws and moreover, it relies on suitable moment closure approximations, which can be difficult to find in practice. In this work we propose a systematic method to derive closed moment dynamics for compartmentalized biochemical systems. We show that for the considered class of systems, the moment equations involve expectations over functions that factorize into two parts, one depending on the molecular content of the compartments and one depending on the compartment number distribution. Our method exploits this structure and approximates each function with suitable polynomial expansions, leading to a closed system of moment equations. We demonstrate the method using three systems inspired by cell populations and organelle networks and study its accuracy across different dynamical regimes., Competing Interests: Declaration of competing interest None., (Copyright © 2023 The Authors. Published by Elsevier Inc. All rights reserved.)

Gene expression is a stochastic and noisy process often occurring in "bursts". Experiments have shown that the compartmentalization of proteins by liquid-liquid phase separation is conducive to reducing the noise of gene expression. Therefore, an important goal is to explore the role of bursts in phase separation noise reduction processes. We propose a coupled model that includes phase separation and a two-state gene expression process. Using the timescale separation method, we obtain approximate solutions for the expectation, variance, and noise strength of the dilute phase. We find that a higher burst frequency weakens the ability of noise reduction by phase separation, but as the burst size increases, this ability first increases and then decreases. This study provides a deeper understanding of phase separation to reduce noise in the stochastic gene expression with burst kinetics., Competing Interests: Declaration of Competing Interest The authors declare no competing interests., (Copyright © 2023 Elsevier Inc. All rights reserved.)

In this paper, we investigate a stochastic SIS epidemic model with logarithmic Ornstein-Uhlenbeck process and generalized nonlinear incidence. Our study focuses on the construction of stochastic Lyapunov functions to establish the threshold condition for the extinction and the existence of the stationary distribution of the stochastic system. We also derive the exact expression of the density function around the quasi-endemic equilibrium, which provides valuable insight into the transmission and progression of the disease within a population. Our findings demonstrate the importance of considering the impact of stochasticity on the spread of epidemics, particularly in the presence of complex incidence mechanisms and stochastic environmental factors. Additionally, the stochastic threshold reveals that ordinary differential equation models and white noise models underestimate the severity of disease outbreaks, while our proposed the stochastic epidemic model with logarithmic Ornstein-Uhlenbeck process accurately captures real-world scenarios., Competing Interests: Declaration of competing interest The authors have no conflicts to disclose., (Copyright © 2023 Elsevier Inc. All rights reserved.)

Understanding how tipping points arise is critical for population protection and ecosystem robustness. This work evaluates the impact of environmental stochasticity on the emergence of tipping points in a predator-prey system subject to the Allee effect and Holling type IV functional response, modeling an environment in which the prey has high group cohesion. We analyze the relationship between stochasticity and the probability and time that predator and prey populations in our model tip between different steady states. We evaluate the safety from extinction of different population values for each species, and accordingly assign extinction warning levels to these population values. Our analysis suggests that the effects of environmental stochasticity on tipping phenomena are scenario-dependent but follow a few interpretable trends. The probability of tipping towards a steady state in which one or both species go extinct generally monotonically increased with noise intensity, while the probability of tipping towards a more favorable steady state (in which more species were viable) usually peaked at intermediate noise intensity. For tipping between two equilibria where a given species was at risk of extinction in one equilibrium but not the other, noise affecting that species had greater impact on tipping probability than noise affecting the other species. Noise in the predator population facilitated quicker tipping to extinction equilibria, whereas prey noise instead often slowed down extinction. Changes in warning level for initial population values due to noise were most apparent near attraction basin boundaries, but noise of sufficient magnitude (especially in the predator population) could alter risk even far away from these boundaries. Our model provides critical theoretical insights for the conservation of population diversity: management criteria and early warning signals can be developed based on our results to keep populations away from destructive critical thresholds., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)

Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be approximated by 'top down' models of dynamics. Here, we study a class of spatially explicit individual-based models with contest competition: where species compete for space in local cells and then disperse to nearby cells. We start by describing simulations of the model, which exhibit large-scale discrete oscillations and characterize these oscillations by measuring spatial correlations. We then develop two new approximate descriptions of the resulting spatial population dynamics. The first is based on local interactions of the individuals and allows us to give a difference equation approximation of the system over small dispersal distances. The second approximates the long-range interactions of the individual-based model. These approximations capture demographic stochasticity from the individual-based model and show that dispersal stabilizes population dynamics. We calculate extinction probability for the individual-based model and show convergence between the local approximation and the non-spatial global approximation of the individual-based model as dispersal distance and population size simultaneously tend to infinity. Our results provide new approximate analytical descriptions of a complex bottom-up model and deepen understanding of spatial population dynamics., Competing Interests: Declaration of competing interest All authors declare that they have no conflicts of interest., (Copyright © 2023 The Author(s). Published by Elsevier Inc. All rights reserved.)

Different types of stochasticity play essential roles in shaping complex population dynamics. This paper presents a novel approach to model demographic and environmental stochasticity in a single-species model with cooperative components that are measured by component Allee effects. Our work provides rigorous mathematical proof on stochastic persistence and extinction, ergodicity (i.e., the existence of a unique stationary distribution) and the existence of a nontrivial periodic solution to study the impacts of demographic and environmental stochasticity on population dynamics. The theoretical and numerical results suggest that stochasticity may affect the population system in a variety of ways, specifically: (i) In the weak Allee effects case (e.g., strong cooperative efforts), the demographic stochasticity from the attack rate contributes to the expansion of the population size, while the demographic stochasticity from the handling rate and the environmental stochasticity have the opposite role, and may even lead to population extinction; (ii) In the strong Allee effects case (cooperative efforts not strong enough), both demographic and environmental stochasticity play a similar role in the survival of population, and are related to the initial population level: if the initial population level is large enough, demographic stochasticity and environmental stochasticity may be detrimental to the survival of population, otherwise if the initial population level is small enough, demographic stochasticity and environmental stochasticity may bring survival opportunities for the population that deterministically would extinct indefinitely; (iii) In the extinction case, demographic and environmental stochasticity cannot change the trend of population extinction, but they can delay or promote population extinction., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Inc. All rights reserved.)

Stochastic chemical kinetics at the single-cell level give rise to heterogeneous populations of cells even when all individuals are genetically identical. This heterogeneity can lead to nonuniform behaviour within populations, including different growth characteristics, cell-fate dynamics, and response to stimuli. Ultimately, these diverse behaviours lead to intricate population dynamics that are inherently multiscale: the population composition evolves based on population-level processes that interact with stochastically distributed single-cell states. Therefore, descriptions that account for this heterogeneity are essential to accurately model and control chemical processes. However, for real-world systems such models are computationally expensive to simulate, which can make optimisation problems, such as optimal control or parameter inference, prohibitively challenging. Here, we consider a class of multiscale population models that incorporate population-level mechanisms while remaining faithful to the underlying stochasticity at the single-cell level and the interplay between these two scales. To address the complexity, we study an order-reduction approximations based on the distribution moments. Since previous moment-closure work has focused on the single-cell kinetics, extending these techniques to populations models prompts us to revisit old observations as well as tackle new challenges. In this extended multiscale context, we encounter the previously established observation that the simplest closure techniques can lead to non-physical system trajectories. Despite their poor performance in some systems, we provide an example where these simple closures outperform more sophisticated closure methods in accurately, efficiently, and robustly solving the problem of optimal control of bioproduction in a microbial consortium model., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Inc. All rights reserved.)