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.
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.
This paper considers the current global issue of containing the coronavirus pandemic as an optimal control problem. The goal is to determine the most advantageous levels of effectiveness of the various control and preventive measures that should be attained in order to cost effectively drive the epidemic towards eradication within a relatively short time. Thus, the problem objective functional is constructed such that it minimizes the prevalence as well as the cost of implementing the various control measures subject to a model for the disease transmission dynamics which incorporates the existing controls. The optimality system of the model is derived based on Pontryagin's maximum principle while the resulting system is solved numerically using the Runge-Kutta fourth order scheme with forward-backward sweep approach. Findings from our results show that the new cases and the prevalence of the disease can be remarkably reduced in a cost effective way, if the specified optimal levels of effectiveness of the various preventive and control measures are upheld continuously for at least a month. Moreover, the results also show that the disease can be eventually eradicated if these effectiveness levels are sustained over a reasonable length of time.
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.
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