Stochastic Extinction Research Articles

Probability of early infection extinction depends linearly on the virus clearance rate.

We provide an in silico study of stochastic viral infection extinction from a pharmacokinetical viewpoint. Our work considers a non-specific antiviral drug that increases the virus clearance rate, and we investigate the effect of this drug on early infection extinction. Infection extinction data are generated by a hybrid multiscale framework that applies both continuous and discrete mathematical approaches. The central result of our paper is the observation, analysis and explanation of a linear relationship between the virus clearance rate and the probability of early infection extinction. The derivation behind this simple relationship is given by merging different mathematical toolboxes.

Preventing evolutionary rescue in cancer.

First-line cancer treatment frequently fails due to initially rare therapeutic resistance. An important clinical question is then how to schedule subsequent treatments to maximize the probability of tumour eradication. Here, we provide a theoretical solution to this problem by using mathematical analysis and extensive stochastic simulations within the framework of evolutionary rescue theory to determine how best to exploit the vulnerability of small tumours to stochastic extinction. Whereas standard clinical practice is to wait for evidence of relapse, we confirm a recent hypothesis that the optimal time to switch to a second treatment is when the tumour is close to its minimum size before relapse, when it is likely undetectable. This optimum can lie slightly before or slightly after the nadir, depending on tumour parameters. Given that this exact time point may be difficult to determine in practice, we study windows of high extinction probability that lie around the optimal switching point, showing that switching after the relapse has begun is typically better than switching too early. We further reveal how treatment dose and tumour demographic and evolutionary parameters influence the predicted clinical outcome, and we determine how best to schedule drugs of unequal efficacy. Our work establishes a foundation for further experimental and clinical investigation of this evolutionarily-informed "extinction therapy" strategy.

Stochastic Persistence, Extinction and Stationary Distribution in HTLV-I Infection Model with CTL Immune Response

Stochastic Persistence, Extinction and Stationary Distribution in HTLV-I Infection Model with CTL Immune Response

Stochastic extinction and persistence of a heterogeneous epidemiological model

Stochastic extinction and persistence of a heterogeneous epidemiological model

Exploring threshold dynamics of a behavioral epidemic model featuring two susceptible classes and second-order jump–diffusion

Understanding and modeling behavioral changes during epidemic outbreaks is crucial for devising effective public health interventions. In this paper, we introduce an enhanced behavioral epidemic model that integrates novel elements to better capture real-world phenomena. Our model incorporates logistic growth as a recruitment rate, reflecting the population’s intrinsic growth constraints. Additionally, we consider two incidence rates to account for varying transmission dynamics. To extend the model’s applicability, we introduce perturbations through second-order jump–diffusion processes, allowing for abrupt changes in population dynamics. We define a threshold parameter based on the properties of an auxiliary system, which distinguishes between the existence of a unique stationary distribution and stochastic extinction. Through numerical simulations, we validate our theoretical findings and demonstrate the impact of nonlinear noise on the model dynamical behavior.

Fungi and deadwood diversity: A test of the area‐heterogeneity trade‐off hypothesis

Abstract Environmental heterogeneity is one of the most fundamental drivers of species diversity. For decades, ecologists have suggested that heterogeneity–diversity relationships are generally positive. But today, a greater variety of heterogeneity–diversity relationships is discussed. In this study, we contrasted two hypotheses for wood‐inhabiting fungi: The classical heterogeneity–diversity hypothesis, which predicts positive relationships due to an increase in niche dimensionality with increasing heterogeneity. And the more recently stated area‐heterogeneity trade‐off hypothesis, that predicts a unimodal pattern due to an inherent trade‐off between the number of occupied niches and the effective area per species. It allows positive and negative relationships only as special cases. We sampled 3715 deadwood objects on 135 plots along a forest structure gradient in the Black Forest, Germany, and recorded 284 wood‐inhabiting fungal species. To assess heterogeneity of deadwood structures, we calculated two multidimensional structural diversity indices: Structural richness was used as a measure of available niche space, and structural divergence as a measure of multivariate variance within that niche space. Those indices were then related to species richness estimates for rare, common and dominant species using the framework of Hill numbers. We found a linear, positive effect of structural richness and a unimodal effect for structural divergence on estimated species diversity. Structural richness, but not structural divergence, was strongly correlated with the number of sampled deadwood objects. No clear differences between the responses of rare, common and dominant species to the two heterogeneity gradients were found. We also estimated the mean abundance as a proxy for mean population size, which decreased significantly with structural richness but was non‐significantly related to structural divergence. Synthesis. In general, the results of this study suggest a unimodal heterogeneity–diversity relationship for deadwood‐inhabiting fungi and are thereby in line with the area‐heterogeneity trade‐off hypothesis. Thus, the negative effect of heterogeneity should lead to lower species richness and a higher risk of stochastic extinctions at high levels of heterogeneity. However, as deadwood amount and deadwood diversity are often strongly correlated, we argue that the positive effect of resource availability on species richness may mask the negative effect of structural heterogeneity in some cases.

Connections between soil microbes, land use and European climate: Insights for management practices

Soil microbial biomass and activity strongly depend on land use, vegetation cover, climate, and soil physicochemical properties. In most cases, this dependence was assessed by one-to-one correlations while by employing network analysis, information about network robustness and the balance between stochasticity and determinism controlling connectivity, was revealed. In this study, we further elaborated on the hypothesis of Smith et al. (2021) that cropland soils depended more on climate variables and therefore are more vulnerable to climate change. We used the same dataset with that of Smith et al. (2021) that contains seasonal microbial, climate and soil variables collected from 881 soil points representing the main land uses in Europe: forests, grassland, cropland. We examined complete (both direct and indirect relationships) and incomplete networks (only direct relationships) and recorded higher robustness in the former. Partial Least Square results showed that on average more than 45% of microbial attributes' variability was predicted by climate and habitat drivers denoting medium to strong effect of habitat filtering. Network architecture slightly affected by season or land use type; it followed the core/periphery structure with positive and negative interactions and no hub nodes. Microbial attributes (biomass, activity and their ratio) mostly belong to core block together with Soil Organic Carbon (SOC), while climate and soil variables to periphery block with the exception of cropland networks, denoting the higher dependence between microbial and climate variables in these latter. All complete networks appeared robust except for cropland and forest in summer, a finding that disagrees with our initial hypothesis about cropland. Networks' connectivity was controlled stronger by stochasticity in forest than in croplands. The lack of human interventions in forest soils increase habitat homogeneity enhancing the influence of stochastic agents such as microbial unlimited dispersal and/or stochastic extinction. The increased stochasticity implies the necessity for proactive management actions.

Global insights into seed dispersal mutualism with cooperative efforts and environmental variability

Seed dispersal mutualisms assume a crucial role in sustaining overall ecosystem functionality. This study extends the foundational framework of seed dispersal mutualism by incorporating animal cooperation and environmental variability. Through the integration of stability theory and phase analysis, we investigate the global dynamics of seed dispersal mutualism in deterministic environments. Theoretical findings reveal that the deterministic system exclusively exhibits equilibrium dynamics, ruling out periodic solutions and chaotic phenomena. Notably, in cases of multiple coexisting equilibria, adjacent equilibria display distinct stability properties. Furthermore, employing stochastic analysis and Lyapunov exponents, we ascertain the uniqueness of global positive solutions in the stochastic model, along with stochastic ultimate boundedness, and precise thresholds for the stochastic persistence and extinction. These results illuminate the theoretical mechanisms governing transitions in seed dispersal mutualism across various stable population levels and underscore the insights into how essential biological factors, including animal cooperation efforts and environmental variability, impact the long-term dynamics of seed dispersal mutualism.

Persistence and Stochastic Extinction in a Lotka–Volterra Predator–Prey Stochastically Perturbed Model

The classical Lotka–Volterra predator–prey model is globally stable and uniformly persistent. However, in real-life biosystems, the extinction of species due to stochastic effects is possible and may occur if the magnitudes of the stochastic effects are large enough. In this paper, we consider the classical Lotka–Volterra predator–prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and, thus, the precise necessary conditions for the stochastic system’s persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type. Therefore, in order to establish the sufficient conditions for extinction, we found the conditions for this stabilization. The analytical results are illustrated by numerical simulations.

Niche Theory as an Underutilized Resource for the Study of Adaptive Radiations.

Biologists are often stuck between two opposing questions: Why are there so many species and why are there not more? Although these questions apply to the maintenance of existing species, they equally apply to the formation of new ones. The more species specialize in terms of their niches, the more opportunities arise for new species to form and coexist in communities. What sets an upper limit to specialization, thus setting an upper limit to speciation? We propose that MacArthur's theories of species packing and resource minimization may hold answers. Specifically, resources and individuals are finite-as species become increasingly specialized, each individual has fewer resources it can access. Species can only be as specialized as is possible in a given resource environment while still meeting basic resource requirements. We propose that the upper limit to specialization lies below the threshold that causes populations to be so small that stochastic extinctions take over, and that this limit is likely rarely approached due to the sequential timing by which new lineages arrive.

Persistence and extinction for stochastic HBV epidemic model with treatment cure rate

With the current struggles of the world nowadays with several epidemics, modeling the dynamics of diseaseoutbreaks has become much more important than any time before. In this context, the present paper aimsat studying a stochastic hepatitis B virus epidemic model with treatment cure rate. Our model consists ofthree epidemic compartments describing the interaction between the susceptible, the infected and the recovered individuals; an SIR model where the infected individuals transmit the infection to the susceptible ones with a transmission rate perturbed by white noise. Our paper begins by establishing that our hepatitis B stochastic model has unique global solution. It moves then to giving sufficient conditions for the stochastic extinction and persistence of the hepatitis B disease. Finally, our paper provides some numerical results to support the analytical study, showing numerically that the treatment cure rate facilitates the extinction of the hepatitis B disease among the population.

Stochastic analysis of two‐strain epidemic model with non‐monotone incidence rates: Application to COVID‐19 pandemic

This work is devoted to the mathematical analysis of a COVID‐19 two‐strain epidemic model. The COVID‐19 mathematical model described the infection forces of each strain by a nonmonotonic incidence function. First, we establish the well‐posedness of the COVID‐19 stochastic model in terms of existence and uniqueness of the global positive solution. After that, we investigate the results of the stochastic extinction and persistence in mean of the COVID‐19 disease. The findings show that both strains of COVID‐19 pandemic extinct, when the basic reproduction number is less than unity. If the latter is not achieved, then the infection related to the strain with higher stochastic basic reproduction number will persist. Additionally, both strains can persist at the same time, if their related stochastic basic reproduction numbers are both greater than one. Finally, various numerical simulations are carried out in order to validate the theoretical findings concerning the extinction and persistence in mean of the disease. As an application of our work, we have chosen to compare our deterministic and stochastic results with COVID‐19 clinical data.

Tipping points emerge from weak mutualism in metacommunities.

The coexistence of obligate mutualists is often precariously close to tipping points where small environmental changes can drive catastrophic shifts in species composition. For example, microbial ecosystems can collapse by the decline of a strain that provides an essential resource on which other strains cross-feed. Here, we show that tipping points, ecosystem collapse, bistability and hysteresis arise even with very weak (non-obligate) mutualism provided the population is spatially structured. Based on numeric solutions of a metacommunity model and mean-field analyses, we demonstrate that weak mutualism lowers the minimal dispersal rate necessary to avoid stochastic extinction, while species need to overcome a mean threshold density to survive in this low dispersal rate regime. Our results allow us to make numerous predictions for mutualistic metacommunities regarding tipping points, hysteresis effects, and recovery from external perturbations, and let us draw general conclusions for ecosystems even with random, not necessarily mutualistic, interactions and systems with density-dependent dispersal rather than direct mutualistic interactions.

Role of seasonal importation and genetic drift on selection for drug-resistant genotypes of Plasmodium falciparum in high-transmission settings.

Historically Plasmodium falciparum has followed a pattern of drug resistance first appearing in low-transmission settings before spreading to high-transmission settings. Several features of low-transmission regions are hypothesized as explanations: higher chance of symptoms and treatment seeking, better treatment access, less within-host competition among clones and lower rates of recombination. Here, we test whether importation of drug-resistant parasites is more likely to lead to successful emergence and establishment in low-transmission or high-transmission periods of the same epidemiological setting, using a spatial, individual-based stochastic model of malaria and drug-resistance evolution calibrated for Burkina Faso. Upon controlling for the timing of importation of drug-resistant genotypes and examination of key model variables, we found that drug-resistant genotypes imported during the low-transmission season were (i) more susceptible to stochastic extinction due to the action of genetic drift, and (ii) more likely to lead to establishment of drug resistance when parasites are able to survive early stochastic loss due to drift. This implies that rare importation events are more likely to lead to establishment if they occur during a high-transmission season, but that constant importation (e.g. neighbouring countries with high levels of resistance) may produce a greater risk during low-transmission periods.

Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin’s saddle-source nature matters

A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations. At low diffusion, the origin is a repulsor, causing the orbits to flow nearly parallel to the axes, risking stochastic extinctions. Higher diffusion turns the repeller into a saddle point. Orbits then quickly converge to the saddle’s unstable manifold, reducing extinction chances. This change in the vector field enhances metapopulation robustness. On the other hand, the well-known fact that asymmetric conditions on the patches is beneficial for the total population is further investigated. This phenomenon has been studied in previous works for large enough or small enough values of the dispersal. In this work, we complete the theory for all values of the dispersal. In particular, we derive analytically a formula for the optimal value of the dispersal that maximizes the total population.

Analysis of a stochastic model for a prey–predator system with an indirect effect

In the current work, we develop and analyse a prey–predator model as a semi-Kolmogorov population model in which the predator has an indirect effect on the prey. The functional response of the model is investigated as Holling type (II). We construct a stochastic environment because of the parameter's random essence to study the influence of environmental fluctuations on this model and introduce a stochastic version of the prey–predator model. Then we present a dynamical analysis of solutions, including existence, uniqueness, positivity, stochastic boundedness, and stochastic extinction of all prey. Finally, some numerical simulations are carried out to validate our theoretical findings and confirm the efficiency and adaptation of our stochastic model.

Transmission dynamics of symptom-dependent HIV/AIDS models.

In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators $ R_0^s $ and $ R_0^e $ were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted.

Asymptotic behaviour of a non‐autonomous multispecies Holling type II model with a complex type of noises

The deterministic non‐autonomous multispecies Holling type II model and its stochastic version with a simple type of noise have been proposed to infer multispecies community structure. However, these models fail to account for complex types of noises, which may render the model overly simplistic. In this paper, a non‐autonomous multispecies Holling type II model with a complex type of noise has been proposed. We establish sufficient conditions for various mathematical properties of the solutions, including existence and uniqueness, stochastic permanence and extinction. Additionally, numerical simulation studies are provided to illustrate our theoretical findings.

DETERMINISTIC AND STOCHASTIC ANALYSIS OF A SIZE-DEPENDENT PHYTOPLANKTON–ZOOPLANKTON MODEL WITH ADDITIVE ALLEE EFFECT

In this paper, a deterministic size-dependent phytoplankton–zooplankton (PZ) model with additive Allee effect as well as its stochastic differential equation version is formulated to explore the growth dynamic of phytoplankton. A stability and Hopf bifurcation analysis is performed towards deterministic PZ model, and stochastic dynamic analysis is carried out on the stochastic PZ model, including the stochastic extinction, persistence in mean and the unique ergodic stationary distribution, which in turn provides a theoretical basis for numerical simulation analysis. Numerical simulations reveal that the synergistic effect of plankton body size and Allee effect can have a complex impact on the growth of phytoplankton in the deterministic and stochastic environments. One of the most interesting findings suggests that the reduced phytoplankton cell size can trigger bistable phenomenon, while the increased phytoplankton cell size or the weakened Allee effect has the ability to destroy such bistable phenomenon.

Dynamical complexity driven by water temperature in a size-dependent phytoplankton–zooplankton model with environmental variability

In this paper, we propose a stochastic phytoplankton–zooplankton (PZ) system modeling the growth dynamic of phytoplankton, where the death rate of zooplankton and the growth rate of phytoplankton are considered to be dependent on water temperature, and random environmental perturbation is characterized by mean-reverting Ornstein–Uhlenbeck process. Mathematical theoretical work mainly studies the stability, persistence, and Hopf bifurcation of deterministic PZ model, as well as analyzes the stochastic extinction, persistence in mean, and ergodic stationary distribution of stochastic PZ model, which provides a theoretical basis for numerical simulations. Numerical simulation work mainly reveals that water temperature plays a crucial role in influencing the dynamic of size-dependent phytoplankton–zooplankton interactions, whether in deterministic or random environments. An important conclusion of this study is that the increase of water temperature is able to induce bubbling effect, however, the small phytoplankton cell size can weaken this bubbling effect, and the large phytoplankton cell size can strengthen this bubbling effect, which supports the experimental conclusion that body size plays a key role in mitigating the negative impact of warming on predator–prey interactions. Further, it is found that the plankton with large body size has the advantages of stable and sustainable survival in the cold environment, while the plankton with small body size has advantages of stable and sustainable survival in the warm environment. Therefore, it can be inferred that plankton will evolve into large body size in the cold environment, but they will evolve into small body size in the warm environment.