VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Did Neoliberalizing West African Forests Produce a New Niche for Ebola?

A recent study introduced a vaccine that controls Ebola Makona, the Zaire ebolavirus variant that has infected 28,000 people in West Africa. We propose that even such successful advances are insufficient for many emergent diseases. We review work hypothesizing that Makona, phenotypically similar to much smaller outbreaks, emerged out of shifts in land use brought about by neoliberal economics. The epidemiological consequences demand a new science that explicitly addresses the foundational processes underlying multispecies health, including the deep-time histories, cultural infrastructure, and global economic geographies driving disease emergence. The approach, for instance, reverses the standard public health practice of segregating emergency responses and the structural context from which outbreaks originate. In Ebola's case, regional neoliberalism may affix the stochastic "friction" of ecological relationships imposed by the forest across populations, which, when above a threshold, keeps the virus from lining up transmission above replacement. Export-led logging, mining, and intensive agriculture may depress such functional noise, permitting novel spillovers larger forces of infection. Mature outbreaks, meanwhile, can continue to circulate even in the face of efficient vaccines. More research on these integral explanations is required, but the narrow albeit welcome success of the vaccine may be used to limit support of such a program.SCOPUS: re.jinfo:eu-repo/semantics/publishe

Outbreak and Extinction Dynamics in Stochastic Populations

Each piece of work herein examines nonlinear population dynamics using methods from deterministic dynamical systems, stochastic processes and statistical mechanics. This dissertation is the compilation of three independent – but related – pieces of work: the first investigates an isolated population that is capable of maintaining multiple carrying capacities; the second project examines a stochastic Ebola model with a zoonotic disease reservoir; and the third looks at a basic disease-invasion model to characterize outbreak vulnerability and the connectedness of supposedly separate populations. Each of these three chapters explore the interplay between interconnected systems, without explicitly modeling the elements that are external to the system of interest. The goal is to take a very large and complex lattice of interconnected biological systems and isolate the necessary components, so that modeling is both practical and utilitarian. These works are done in either an ecological or an epidemiological context, but the results in each chapter can be broadly applied to outbreak, invasion, extinction, and connectedness in stochastic population modeling. i

Global stability of a fractional-order logistic growth model with infectious disease

Infectious disease has an influence on the density of a population. In this paper, a fractional-order logistic growth model with infectious disease is formulated. The population grows logistically and divided into two compartments i.e. susceptible and infected populations. We start by investigating the existence, uniqueness, non-negativity, and boundedness of solutions. Furthermore, we show that the model has three equilibrium points namely the population extinction point, the disease-free point, and the endemic point. The population extinction point is always a saddle point while others are conditionally asymptotically stable. For the non-trivial equilibrium points, we successfully show that the local and global asymptotic stability have the similar properties. Especially, when the endemic point exists, it is always globally asymptotically stable. We also show the existence of forward bifurcation in our model. We portray some numerical simulations consist of the phase portraits, time series, and a bifurcation diagram to validate the analytical findings

2015 Conference Abstracts: Annual Undergraduate Research Conference at the Interface of Biology and Mathematics

Schedule and abstract book for the Seventh Annual Undergraduate Research Conference at the Interface of Biology and Mathematics Date: November 21-22, 2015Plenary speaker: Robert Smith, University of OttawaFeatured speaker: Rachel Lenhart, University of Wisconsin, Madiso

Analysis of a model for waterborne diseases with Allee effect on bacteria

A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission. The existence and stability of biologically meaningful equilibria is investigated through a detailed discussion of both backward and Hopf bifurcations. The sensitivity analysis of the basic reproduction number is performed. Numerical simulations confirming the obtained results in two different scenarios are shown

Did Ebola emerge in West Africa by a policy-driven phase change in agroecology? Ebola's social context

SCOPUS: no.jinfo:eu-repo/semantics/publishe

STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH APPLICATIONS IN ECOLOGY AND EPIDEMICS

Mathematical modeling with delay differential equations (DDEs) is widely used for analysis and predictions in various areas of life sciences, such as population dynamics, epidemiology, immunology, physiology, and neural networks. The memory or time-delays, in these models, are related to the duration of certain hidden processes like the stages of the life cycle, the time between infection of a cell and the production of new viruses, the duration of the infectious period, the immune period, and so on. In ordinary differential equations (ODEs), the unknown state and its derivatives are evaluated at the same time instant. In DDEs, however, the evolution of the system at a certain time instant depends on the past history/memory. Introduction of such time-delays in a differential model significantly improves the dynamics of the model and enriches the complexity of the system. Moreover, natural phenomena counter an environmental noise and usually do not follow deterministic laws strictly but oscillate randomly about some average values, so that the population density never attains a fixed value with the advancement of time. Accordingly, stochastic delay differential equations (SDDEs) models play a prominent role in many application areas including biology, epidemiology and population dynamics, mostly because they can offer a more sophisticated insight through physical phenomena than their deterministic counterparts do. The SDDEs can be regarded as a generalization of stochastic differential equations (SDEs) and DDEs.This dissertation, consists of eight Chapters, is concerned with qualitative and quantitative features of deterministic and stochastic delay differential equations with applications in ecology and epidemics. The local and global stabilities of the steady states and Hopf bifurcations with respect of interesting parameters of such models are investigated. The impact of incorporating time-delays and random noise in such class of differential equations for different types of predator-prey systems and infectious diseases is studied. Numerical simulations, using suitable and reliable numerical schemes, are provided to show the effectiveness of the obtained theoretical results.Chapter 1 provides a brief overview about the topic and shows significance of the study. Chapter 2, is devoted to investigate the qualitative behaviours (through local and global stability of the steady states) of DDEs with predator-prey systems in case of hunting cooperation on predators. Chapter 3 deals with the dynamics of DDEs, of multiple time-delays, of two-prey one-predator system, where the growth of both preys populations subject to Allee effects, with a direct competition between the two-prey species having a common predator. A Lyapunov functional is deducted to investigate the global stability of positive interior equilibrium. Chapter 4, studies the dynamics of stochastic DDEs for predator-prey system with hunting cooperation in predators. Existence and uniqueness of global positive solution and stochastically ultimate boundedness are investigated. Some sufficient conditions for persistence and extinction, using Lyapunov functional, are obtained. Chapter 5 is devoted to investigate Stochastic DDEs of three-species predator prey system with cooperation among prey species. Sufficient conditions of existence and uniqueness of an ergodic stationary distribution of the positive solution to the model are established, by constructing a suitable Lyapunov functional. Chapter 6 deals with stochastic epidemic SIRC model with time-delay for spread of COVID-19 among population. The basic reproduction number ℛs0 for the stochastic model which is smaller than ℛ0 of the corresponding deterministic model is deduced. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov functional, and conditions for the extinction of the disease are obtained. In Chapter 7, some numerical schemes for SDDEs are discussed. Convergence and consistency of such schemes are investigated. Chapter 8 summaries the main finding and future directions of research. The main findings, theoretically and numerically, show that time-delays and random noise have a significant impact in the dynamics of ecological and biological systems. They also have an important role in ecological balance and environmental stability of living organisms. A small scale of white noise can promote the survival of population; While large noises can lead to extinction of the population, this would not happen in the deterministic systems without noises. Also, white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can also occur due to the time-delay in the transmission terms