a b s t r a c tWith a five dimensional system of ordinary differential equations based on the SIR and SIS models, we consider the dynamics of epidemics in a community which consists of residents and short-stay visitors. Taking different viewpoints to consider public health policies to control the disease, we derive different basic reproduction numbers and clarify their common/different mathematical natures so as to understand their meanings in the dynamics of the epidemic. From our analyses, the short-stay visitor subpopulation could become significant in determining the fate of diseases in the community. Furthermore, our arguments demonstrate that it is necessary to choose one variant of basic reproduction number in order to formulate appropriate public health policies.

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The novel coronavirus (COVID-19) pandemic continues despite series of control measures implemented to curtail it. Therefore, it is pertinent to study how the various proposed control measures can be effectively combined in order to stem the alarming spread of the disease and its attendant consequences. In this paper, a deterministic model for the transmission dynamics of the disease, which incorporates the impacts of the various implemented control measures, is presented. Based on the proposed model, the disease’s basic reproduction number (R0) was derived and the equilibrium solutions were determined. It was shown that whenever R0 \(\le\) 1, the model has only the disease-free equilibrium which is globally stable while in circumstances where R0 > 1, there exists an endemic equilibrium which is globally asymptotically stable. When the latter equilibrium state exists, the former becomes unstable. In addition, the model parameters were estimated using Nigeria’s demographic and COVID-19 surveillance data. The model is simulated for different scenarios of the disease outbreak and the results suggest that the disease will die out quickly in the population if about half of the population adhere to personal protection, about half of exposed individuals are efficiently traced and about half of symptomatic individuals are promptly isolated and treated.

The ability of humans to generate numbers that are really random has always been a subject of debate. This paper investigated the possibility for a group of humans to serve as random number generators. A total of 2344 students, who were not pre-informed to avoid bias, from different faculties within the Federal University of Technology Akure were asked to chose a random number between 1 and 10. Using various statistical tests, we sought answers to the possibility of predictors like participant’s test score, gender, age and school influencing their choice of random numbers. We discovered that the numbers generated are highly random and chaotic despite number 1 being the most selected number across all predictors that was considered. Our study found that gender, test score, age did not significantly influence the choice of number while faculty showed a significant relation α < 0.05.

We introduce a class of analytic functions which is defined in terms of a quasi-subordination. Coefficient estimates including the relevant classical Fekete–Szegö inequality of functions belonging to the aforementioned class are derived. Improved results for associated classes involving subordination and majorization are also discussed.