Evolutionary game dynamics of combining two different aspiration-driven update rules in structured populations

In evolutionary games,most studies on finite populations have focused on a single updating mechanism.However,given the differences in individual cognition,individuals may change their strategies according to different updating mechanisms.For this reason,we consider two different aspiration-driven updating mechanisms in structured populations:satisfied-stay unsatisfied shift(SSUS)and satisfied-cooperate unsatisfied defect(SCUD).To simulate the game player’s learning process,this paper improves the particle swarm optimization algorithm,which will be used to simulate the game player’s strategy selection,i.e.,population particle swarm optimization(PPSO)algorithms.We find that in the prisoner’s dilemma,the conditions that SSUS facilitates the evolution of cooperation do not enable cooperation to emerge.In contrast,SCUD conditions that promote the evolution of cooperation enable cooperation to emerge.In addition,the invasion of SCUD individuals helps promote cooperation among SSUS individuals.Simulated by the PPSO algorithm,the theoretical approximation results are found to be consistent with the trend of change in the simulation results.

GENERALIZED OPERATORS AND P(φ)_2 QUANTUM FIELDS

In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.

Post-Optimality Analysis of Energy Consumption Model and Utility Application

Problems associated with energy distribution, consumption and management are undoubtedly some of the most significant problems that energy utilities face globally. For instance, when development takes place, the demand for electrical power and in particular domestic electrical energy also increases. Thus improvement of energy distribution policies becomes important for utilities and energy decision making agencies. The authors had earlier [1] [2] provided a mixed strategy 2-player game model for a residential energy consumption profile for winter and summer seasons of the year using a dual-occupancy high-rise (11-storey) building located within the Polytechnic of Namibia, Windhoek. The optimum energy values and the corresponding probabilities obtained from the model extend the usual simple statistical analyses of minimum and maximum energy values and their associated percentages. The time-block and the week-day strategies depict critical probabilistic values worth considering for decision purposes, especially, the necessity and justification for a dual tariff regime for the residential and workplace residents of the building as against the existing institutional uniform energy tariff policy. However, this paper presents extended results of post-optimality analyses for the winter and summer seasons, and thus provides the optimal range of energy values over which the energy consumption can change without changing the optimal tariff estimate parameters obtained from the mixed strategy of critical energy game values. The post-optimality analyses also provide extended information on the mixed strategy of non-optimal week-day solutions obtained from the game model, hence validating one of the essential roles of sensitivity analysis, namely, investigation of sub-optimal solutions. From application point of view, the post-optimality model provides a useful tool for Utilities, especially for identifying flexibility range of optimal break-even energy values for consumers, such as in the informal settlements where metering is rather a challenge to determine varied or non-uniform tariffs.

A Retrospective Study of the Variability in Etiological Agents of Urinary Tract Infections among Patients in Windhoek-Namibia

Urinary tract infections (UTIs) are one of the most common infections that affect patients of both genders of all age groups. The common bacteria causing UTIs have not yet been identified in Namibia. Due to empirical treatment in the country, antibiotic resistance might be on the rise. The objective of the study was to identify the organisms that frequently caused UTIs, and the antibiotic sensitivity patterns of the bacteria isolated. A retrospective analysis was performed on 20,438 urine results submitted to the Namibia Institute of pathology (NIP), the public health laboratory in the country from January 2012 to December 2012. The raw data from NIP was compiled using Microsoft Excel. It was then imported to the IBM SPSS 22 statistical program for further analysis. The results showed that there were 3865 (18.9%) UTI cases due to Escherichia coli making it the most prevalent organism isolated, followed by Proteus mirabilis 758 (3.7%), Enterococcus faecalis 706 (3.5%) and Klebsiella pneumoniae 640 (3.1%). Female patients were more affected by UTIs than males. The eleven most common causes of UTIs in this study were mostly isolated from females. The most common cause of urinary tract infections in males was Extended Spectrum Beta Lactamase (ESBL) Klebsiella pneumoniae. The drugs to which these common organisms were resistant to were amoxicillin and cotrimoxazole (SXT). Cefapime, ofloxacin and piptaze were the most effective antibiotics in this study. There were 6 cases of UTIs due to Mycobacterium tuberculosis and 10 cases due to Schistosoma haematobium. The most common UTI etiology in Windhoek was Escherichia coli. Most of the isolates were resistant to at least one antibiotic, with ESBL organisms having resistance to more than ten antibiotics.

Infinitely Many Solutions for a Class of Quasi-linear Elliptic Problem

In this paper,we study the following quasi-linear elliptic equation:■where Ω?R^(N) is a bounded domain,λ>0 is a parameter.The function ψ(|t|)t is the subcritical term,and φ(|t|)t is the critical Orlicz-Sobolev growth term with respect to φ.Under appropriate conditions on φ,ψ and φ,we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation,for λ∈(0,λ_(0)),where λ_(0)> 0 is a fixed constant.

A PERISHABLE INVENTORY SYSTEM WITH SERVICE FACILITIES, MAP ARRIVALS AND PH- SERVICE TIMES

We consider a continuous review perishable （s,S） inventory system with a service facility consisting of a waiting hall of finite capacity and a single server. We assume two types of customers, ordinary and negative, arrive according to a Markovian Arrival Process （MAP）. An ordinary customer joins the queue and a negative customer instead of joining the queue removes one ordinary customer from the queue. The removal rule adopted in this paper is RCE （removal of a customer from the end）. The individual customer＇s unit demand is satisfied after a random time of service which is assumed to have a phase-type distribution. The life time of each item and the lead time of the reorders have been assumed to be independent exponential distributions. The joint probability distribution of the number of customers in the system and the inventory level is obtained for the steady state case. Various stationary system performance measures are computed and the total expected cost rate is calculated. The results are illustrated numerically.

A malaria model with Caputo-Fabrizio and Atangana-Baleanu derivatives

In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered.Using Lyapunov theory,we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model,and the fractional models,whenever the basic reproduction number R0 is greater than one.By using fixed point theory,we prove existence,and conditions of the uniqueness of solutions,as well as the stability and convergence of numerical schemes.Numerical simulations for both models,using fractional Euler method and Adams–Bashforth method,respectively,are provided to confirm the effectiveness of used approximation methods for different values of the fractional-orderγ.

On the existence and uniqueness of a nonlinear q-difference boundary value problem of fractional order

In this research collection,we estimate the existence of the unique solution for the boundary value problem of nonlinear fractional q-difference equation having the given form c D^(ζ)_(q) v(t)−h(t,v(t))=0,0≤t≤1,α_(1)v(0)+β_(1)D_(q)v(0)=v(η1),α_(2)v(1)−β_(2)D_(q)v(1)=v(η2),where 1<ζ≤2,(η1,η2)∈(0,1)^(2),α_(i),β_(i)∈R(i=1,2),h∈C([0,1]×R,R)and c Dζq represents the Caputo-type nonclassical q-derivative of orderζ.We use well-known principal of Banach contraction,and Leray–Schauder nonlinear alternative to vindicate the unique solution existence of the given problem.Regarding the applications,some examples are solved to justify our outcomes.

Generalized T3-plot for testing high-dimensional normality

A new dimension-reduction graphical method for testing high- dimensional normality is developed by using the theory of spherical distributions and the idea of principal component analysis. The dimension reduction is realized by projecting high-dimensional data onto some selected eigenvector directions. The asymptotic statistical independence of the plotting functions on the selected eigenvector directions provides the principle for the new plot. A departure from multivariate normality of the raw data could be captured by at least one plot on the selected eigenvector direction. Acceptance regions associated with the plots are provided to enhance interpretability of the plots. Monte Carlo studies and an illustrative example show that the proposed graphical method has competitive power performance and improves the existing graphical method significantly in testing high-dimensional normality.

A mathematical study of a tuberculosis model with fractional derivatives

In this work,we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis(TB)model with two fractional derivatives,namely,Caputo–Fabrizio fractional derivative and the new generalized Caputo fractional derivative.We begin by recalling some existing results such as the basic reproduction number R0 and the equilibrium points of the model.Then,we study the global asymptotic stability of disease-free equilibrium of the fractional models.We also prove,for each fractional model,the existence and uniqueness of solutions.An iterative solution of the two models is computed using the Predictor–Corrector method.Using realistic parameter values,we perform numerical simulations for different values of the fractional order.Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo–Fabrizio fractional derivative and the classical integer-order TB model.

Lassa hemorrhagic fever model using new generalized Caputo-type fractional derivative operator

In some of the previous decades, we have observed that mathematical modeling hasbecome one of the most interesting research fields and has attracted many researchers.In this regard, thousands of researchers have proposed different varieties of mathematicalmodels to study the dynamics of a number of real-world problems. This research workis framed to analyzing the structure of the well-known Lassa hemorrhagic epidemic;adangerous epidemic for pregnant women, via new generalized Caputo type nonintegerorder derivative with the help of a modified Predictor–Corrector scheme. Lassa hemorrhagic disease is an epidemical and biocidal fever, whose negative impacts were initiallyrecognized in the countries of Africa. This virus has killed many pregnant women ascompared to the Ebola epidemic. It was noticed that Lassa virus was isolated in Verocell cultures from a blood pattern, and after 12 days it was ejective, after the climb ofthe sickness. In this research study, necessary theorems and lemmas are reminded toprove the existence of a unique solution and stability of given fractional approximationscheme. All necessary results are reminded to confirm the effectiveness of the proposedapproximation algorithm by graphical observations for various fractional-order values.In our practical calculations, we plotted the graphs for two different values of naturaldeath rate along with various values of given fractional-order operator. Our major target is to show the importance of the proposed modified version of the Predictor–Correctoralgorithm in epidemic studies by exploring the given Lassa hemorrhagic fever dynamics.

Prediction studies of the epidemic peak of coronavirus disease in Japan: From Caputo derivatives to Atangana-Baleanu derivatives

New atypical pneumonia caused by a virus called Coronavirus(COVID-19)appeared in Wuhan,China in December 2019.Unlike previous epidemics due to the severe acute respiratory syndrome(SARS)and the Middle East respiratory syndrome coronavirus(MERS-CoV),COVID-19 has the particularity that it is more contagious than the other previous ones.In this paper,we try to predict the COVID-19 epidemic peak in Japan with the help of real-time data from January 15 to February 29,2020 with the uses of fractional derivatives,namely,Caputo derivatives,the Caputo–Fabrizio derivatives,and Atangana–Baleanu derivatives in the Caputo sense.The fixed point theory and Picard–Lindel of approach used in this study provide the proof for the existence and uniqueness analysis of the solutions to the noninteger-order models under the investi-gations.For each fractional model,we propose a numerical scheme as well as prove its stability.Using parameter values estimated from the Japan COVID-19 epidemic real data,we perform numerical simulations to confirm the effectiveness of used approxima-tion methods by numerical simulations for different values of the fractional-orderγ,and to give the predictions of COVID-19 epidemic peaks in Japan in a specific range of time intervals.