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In the past few decades, the discrete dynamics of difference maps have attained the remarkable attention of researchers owing to their incredible applications in different domains, like cryptography, secure communications, weather forecasting, traffic flow models, neural network models, and population biology. In this article, a generalized chaotic system is proposed, and superior dynamics is disclosed through fixed point analysis, time-series evolution, cobweb representation, period-doubling, period-3 window, and Lyapunov exponent properties. The comparative bifurcation and Lyapunov plots report the superior stability and chaos performance of the generalized system. It is interesting to notice that the generalized system exhibits superior dynamics due to an additional control parameter β . Analytical and numerical simulations are used to explore the superior dynamical characteristics of the generalized system for some specific values of parameter β . Further, it is inferred that the superiority in dynamics of the generalized system may be efficiently used for better future applications. [ABSTRACT FROM AUTHOR]

A leading crisis in the United States is the opioid use disorder (OUD) epidemic. Opioid overdose deaths have been increasing, with over 100,000 deaths due to overdose from April 2020 to April 2021. This paper presents a mathematical model to address illicit OUD (IOUD), initiation, casual use, treatment, relapse, recovery, and opioid overdose deaths within an epidemiological framework. Within this model, individuals remain in the recovery class unless they relapse back to use and due to the limited availability of specialty treatment facilities for individuals with OUD, a saturation treatment function was incorporated. Additionally, a casual user class and its corresponding specialty treatment class were incorporated. We use both heroin and all-illicit opioids datasets to find parameter estimates for our models. Bistability of equilibrium solutions was found for realistic parameter values for the heroin-only dataset. This result implies that it would be beneficial to increase the availability of treatment. An alarming effect was discovered about the high overdose death rate: by 2046, the disorder-free equilibrium would be the only stable equilibrium. This consequence is concerning because it means the epidemic would end due to high overdose death rates. The IOUD model with a casual user class, its sensitivity results, and the comparison of parameters for both datasets, showed the importance of not overlooking the influence that casual users have in driving the all-illicit opioid epidemic. Casual users stay in the casual user class longer and are not going to treatment as quickly as the users of the heroin epidemic. Another result was that the users of the all-illicit opioids were going to the recovered class by means other than specialty treatment. However, the change in the relapse rate has more of an influence for those individuals than in the heroin-only epidemic. The results above from analyzing this model may inform health and policy officials, leading to more effective treatment options and prevention efforts.

Colletotrichum coccodes (Wallr.) Hughes is an asexual fungus with five vegetative compatibility groups. It was postulated that C. coccodes was isolated at the center of origin of potato at one time, and due to the movement of potato around the globe, the fungus was established on each continent but became bottlenecked and genetically unable to form stable heterokaryons via vegetative compatibility grouping (VCG) studies. The objectives of this study were (i) to determine if the VCGs around the world are related to the VCGs in Chile, (ii) to determine the diversity of C. coccodes populations in Chile, and (iii) to find any evidence for a cryptic sexual life cycle for this fungus. Worldwide C. coccodes populations have been found to be genetically correlated and belong to one or more C. coccodes-identified VCGs. The most distributed VCG in Chile was VCG2, which is the most common VCG in North America. We hypothesize that one or more VCGs had spread from Chile to the rest of the world. Precautions and further studies should be investigated by using other molecular markers and gene sequencing. [ABSTRACT FROM AUTHOR]