Dynamics of a stochastic population model with Allee effect and jumps

This paper is concerned with a stochastic population model with Allee effect and jumps. First, we show the global existence of almost surely positive solution to the model. Next, exponential extinction and persistence in mean are discussed. Then, we investigated the global attractivity and stability in distribution. At last, some numerical results are given. The results show that if attack rate $a$ is in the intermediate range or very large, the population will go extinct. Under the premise that attack rate $a$ is less than growth rate $r$, if the noise intensity or jump is relatively large, the population will become extinct; on the contrary, the population will be persistent in mean. The results in this paper generalize and improve the previous related results.

A Proposed Methodology for Modelling the Solvency of a National Pension Scheme

The main aim of this study is to fit a model for predicting pension liability. The study proposed a stochastic population model to determine the status of a pension scheme. By categorizing the members of the Social Security and National Insurance Trust (SSNIT) pension scheme of Ghana into five groups, the birth and death process with emigration and the pure death process coupled with assumption of the Yule’s process, were combined to successfully formulate a model for forecasting the surplus of SSNIT to be used as a proxy for assessing the solvency status of the scheme. The reliability of the proposed model was corroborated by very high coverage probabilities of the estimates of expected surpluses produced. The study demonstrated how easy it is to use the proposed model to carry out sensitivity analysis which allows the exploration of various scenarios leading to formulation and implementation of policies to enhance the solvency of the scheme. One major advantage of the proposed model is that, it uses more information (variables) compared to others proposed elsewhere for the same purpose. This contributes to the precision of estimates from the model. A key finding of the study is that SSNIT would have still been solvent had she increased pension by 50%.

Extinction time of the logistic process

The logistic birth and death process is perhaps the simplest stochastic population model that has both density-dependent reproduction and a phase transition, and a lot can be learned about the process by studying its extinction time, $\tau_n$ , as a function of system size n. A number of existing results describe the scaling of $\tau_n$ as $n\to\infty$ for various choices of reproductive rate $r_n$ and initial population $X_n(0)$ as a function of n. We collect and complete this picture, obtaining a complete classification of all sequences $(r_n)$ and $(X_n(0))$ for which there exist rescaling parameters $(s_n)$ and $(t_n)$ such that $(\tau_n-t_n)/s_n$ converges in distribution as $n\to\infty$ , and identifying the limits in each case.

Consciousness, decision making, and volition: freedom beyond chance and necessity

What is the role of consciousness in volition and decision-making? Are our actions fully determined by brain activity preceding our decisions to act, or can consciousness instead affect the brain activity leading to action? This has been much debated in philosophy, but also in science since the famous experiments by Libet in the 1980s, where the current most common interpretation is that conscious free will is an illusion. It seems that the brain knows, up to several seconds in advance what “you” decide to do. These studies have, however, been criticized, and alternative interpretations of the experiments can be given, some of which are discussed in this paper. In an attempt to elucidate the processes involved in decision-making (DM), as an essential part of volition, we have developed a computational model of relevant brain structures and their neurodynamics. While DM is a complex process, we have particularly focused on the amygdala and orbitofrontal cortex (OFC) for its emotional, and the lateral prefrontal cortex (LPFC) for its cognitive aspects. In this paper, we present a stochastic population model representing the neural information processing of DM. Simulation results seem to confirm the notion that if decisions have to be made fast, emotional processes and aspects dominate, while rational processes are more time consuming and may result in a delayed decision. Finally, some limitations of current science and computational modeling will be discussed, hinting at a future development of science, where consciousness and free will may add to chance and necessity as explanation for what happens in the world.

Dynamics of a stochastic population model with predation effects in polluted environments

The present paper puts forward and probes a stochastic single-species model with predation effect in a polluted environment. We propose a threshold between extermination and weak persistence of the species and provide sufficient conditions for the stochastic persistence of the species. In addition, we evaluate the growth rates of the solution. Theoretical findings are expounded by some numerical simulations.

A stochastic population model of cholera disease

<p style='text-indent:20px;'>A cholera population model with stochastic transmission and stochasticity on the environmental reservoir of the cholera bacteria is presented. It is shown that solutions are well-behaved. In comparison with the underlying deterministic model, the stochastic perturbation is shown to enhance stability of the disease-free equilibrium. The main extinction theorem is formulated in terms of an invariant which is a modification of the basic reproduction number of the underlying deterministic model. As an application, the model is calibrated as for a certain province of Nigeria. In particular, a recent outbreak (2019) in Nigeria is analysed and featured through simulations. Simulations include making forward projections in the form of confidence intervals. Also, the extinction theorem is illustrated through simulations.</p>