In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability and the Fokker–Planck equation for fish population [Formula: see text]. In the Gaussian case, these quantities satisfy local partial differential equations while in the non-Gaussian case, they satisfy nonlocal partial differential equations. Following a discussion of existence, uniqueness and stability, we calculate numerical approximations of the solutions of those equations. For each noise model we then compare the behaviors of the mean time to extinction and the solution of the Fokker–Planck equation as growth rate [Formula: see text], carrying capacity [Formula: see text], intensity of Gaussian noise [Formula: see text], noise intensity [Formula: see text] and stability index [Formula: see text] vary. The MET from the interval [Formula: see text] at the right boundary is finite if [Formula: see text]. For [Formula: see text], the MET from [Formula: see text] at this boundary is infinite. A larger stability index [Formula: see text] is less likely leading to the extinction of the fish population.

This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic differential equation driven by multiplicative Gaussian noise. With the help of the associated Fokker–Planck equation, we analyze the population extinction probability and the probability of reaching a large population size before reaching a small one. We further study the impact of the harvest rate, noise intensity and the Allee effect on population evolution. The analysis and numerical experiments show that if the noise intensity and harvest rate are small, the population grows exponentially, and upon reaching the carrying capacity, the population size fluctuates around it. In the stochastic logistic-harvest model without the Allee effect, when noise intensity becomes small (or goes to zero), the stationary probability density becomes more acute and its maximum point approaches one. However, for large noise intensity and harvest rate, the population size fluctuates wildly and does not grow exponentially to the carrying capacity. So as far as biological meanings are concerned, we must catch at small values of noise intensity and harvest rate. Finally, we discuss the biological implications of our results.

For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by ξ which depends on white and jump noises. The effects of these noises on the dynamics of the model are studied. The numerical experiments show that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterpart. In other words, the impact of the noises on the extinction and persistence is high. When the noise is large or small, our numerical findings show that COVID-19 vanishes from the population if $\xi <1$ ξ < 1 ; whereas the epidemic cannot go out of control if $\xi >1$ ξ > 1 . From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., we can conclude that the stochastic model is more realistic than the deterministic one. Finally, to illustrate this phenomenon, we put some numerical simulations.

In this work we study the impact of non-Gaussian α-stable Lévy motion on transitions between metastable equilibrium states (or attractors) in a stochastic Stommel two-box model for thermohaline circulation (THC). By maximizing probability density of the solution process associated with a nonlocal Fokker-Planck equation, we compute maximal likely pathways and identify corresponding maximal likely stable equilibrium states. Our numerical results indicate weakened THC may be induced by perturbation with very small noise intensity in certain range of stability index. Moreover, larger noise intensity and larger stability index induce weakened THC within shorter bifurcation time.

This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic differential equation driven by multiplicative Gaussian noise. With the help of the associated Fokker-Planck equation, we analyze the population extinction probability and the probability of reaching a large population size before reaching a small one. We further study the impact of the harvest rate, noise intensity, and the Allee effect on population evolution. The analysis and numerical experiments show that if the noise intensity and harvest rate are small, the population grows exponentially, and upon reaching the carrying capacity, the population size fluctuates around it. In the stochastic logistic-harvest model without the Allee effect, when noise intensity becomes small (or goes to zero), the stationary probability density becomes more acute and its maximum point approaches one. However, for large noise intensity and harvest rate, the population size fluctuates wildly and does not grow exponentially to the carrying capacity. So as far as biological meanings are concerned, we must catch at small values of noise intensity and harvest rate. Finally, we discuss the biological implications of our results.

Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic bifurcation techniques are infrequently employed. Here we establish stochastic P-bifurcation behavior of (i) a growth model with state dependent birth rate and constant death rate, and (ii) a logistic growth model with state dependent carrying capacity, both of which are driven by multiplicative symmetric stable Lévy noise. Transcritical bifurcation occurs in the deterministic counterpart of the first model, while saddle-node bifurcation takes place in the logistic growth model. We focus on the impact of the variations of the growth rate, the per capita daily adult mortality rate, the stability index, and the noise intensity on the stationary probability density functions of the associated non-local Fokker-Planck equation. Implications of these bifurcations in population dynamics are discussed. In the first model the bifurcation parameter is the ratio of the population birth

Background. Though there is an effective intervention, pain after surgical intervention is undermanaged worldwide. A systematic implementation is required to increase the utilization of available evidence-based intervention to manage the inevitable pain after surgery. The aim of this research project is to develop a scalable model for managing pain after cesarean section by implementing the World Health Organization’s (WHO) pain management guidelines through a combination of implementation research and quality improvement methods. Methods. We implemented the World Health Organization (WHO) pain management guidelines using effective implementation strategies. First, we conducted a formative qualitative exploration to identify enablers and obstacles. In addition, we took base-line assessment on pain management implementation process and outcome using a checklist prepared from the guideline and an adapted American Pain Outcome assessment tool version 2010, respectively. Then, we integrated the guidelines into the existing practice by using collaborative iterative learning strategy. We analyzed the data by Statistical Packages for Social Sciences (SPSS) version 21. We compared the before and after data using chi-squared and Fischer’s exact test. A change in any measurement was considered as significant at p value 0.05. Result. We collected data from 106 mothers before and 110 mothers after intervention implementation. We successfully integrated pain as a fifth vital sign in more than 87% (p value <0.001) of patient, and fidelity was approximately 59% (p value <0.001). In addition, we significantly improved pain outcome measures after the implementation of the intervention. Conclusion and Recommendations. A systematic approach to implement pain management guidelines was successful. We recommend the ward sustain these gains and that hospital, the region, and the nation to replicate the success.

Abstract. How will extreme events due to human activities and climate change affect the oceanic thermohaline circulation is a key concern in climate predictions. The stability of the thermohaline circulation with respect to extreme events, such as fresh-water oscillations, greenhouse gas accumulations and collapse of the Atlantic meridional overturning circulation, is examined using a conceptual stochastic Stommel two-compartment model. The extreme fluctuations are modeled by symmetric α-stable Lévy motions whose pathways are cádlág functions with at most a countable number of jumps. The mean first passage time, escape probability and stochastic basin of attraction are used to perform the stability analysis of on (off) equilibrium states. Our results argue that for model with weak fresh-water forcing strength, the greatest threat to the stability of the on-state represents noise with low jumps and higher frequency that can be seen as civilization-induced greenhouse gas accumulation. On the other hand, the off-state stability is more vulnerable to the agitations with moderate jumps and frequencies which can be interpreted as wind- driven circulations towards higher latitudes. Under the repercussion of stochastic noise, on to off transitions are more expected in the model if the fresh-water influx is strong. Moreover, transitions from one metastable state to another are equiprobable when the fresh-water input induces a symmetric potential well.