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This paper introduces a deterministic fractional-order epidemic model (FOEM) for studying the transmission dynamics of the human immunodeficiency virus (HIV) and acquired immunodeficiency syndrome (AIDS). The model highlights the substantial role of unaware and undetected HIV-infected individuals in spreading the disease. Control strategies, such as wielding condoms, level of preventive measures to avoid infection, and self-strictness of susceptibles in sexual contact, have been incorporated into the study. The basic reproduction number ℛ 0 α has been derived, which suggests the conditions for ensuring the persistence and elimination of the disease. Further, to validate the model, actual HIV data taken from Mexico and India separately have been used. The disease dynamics and its control in both countries are analyzed broadly. The values of biological parameters are estimated at which numerical solutions better match the actual data of HIV patients in the case of fractional-order (FO) instead of integer-order (IO). Moreover, in the light of ℛ 0 α , our findings forecast that the disease will abide in the population in Mexico, and at the same time, it will die out from India after a long time. [ABSTRACT FROM AUTHOR]

This paper studies the effect of habitat complexity on Greater one-horned rhinoceros (Rhinoceros unicornis) and tiger (Panthera tigris) population model in Kaziranga National Park (KNP), Assam, India. Based on the analysis of the data collected from PCCF, Wildlife, Assam, three mathematical models are formulated and studied. In view of ecology, the main objective of the study is to increase the size of rhino population in aforesaid park. The mathematical stability and the complex dynamical behavior of systems are analyzed here. In KNP, the immature rhinos are killed by tiger, so the first system describes a stage structured prey–predator interaction , where the rhino is the prey and is divided into immature (horn not developed) and mature (horn developed) category and the tiger is the predator. The immature rhino is killed by the tiger following Holling type-II functional response, while the mature rhino falls prey to human induced poaching activities [Source: PCCF Wildlife, Assam, India]. Though Kaziranga is famous all over the world for the Greater one-horned rhinoceros, many other herbivores are also present in really good number and the tiger preys on them too. Thus, the previous system is modified by modifying the Holling type-II functional response incorporating the effect of additional food availability. To increase the number of rhino and to maintain the ecological balance of KNP, the second system is further extended by introducing habitat complexity in the Holling type-II functional response. In each system, equilibrium points have been obtained and their stability are discussed. Finally, numerical simulations are carried out to illustrate the analytical results. Based on the simulation results, it can be stated that the size of the rhino population increases in the presence of additional food and habitat complexity in spite of the poaching activities to a certain extent. The system shows complex dynamical behavior like Hopf bifurcation with respect to Poaching activity. Sensitivity analysis with respect to four important parameters viz., poaching effect, quality and quantity of the additional food and habitat complexity is also discussed. [ABSTRACT FROM AUTHOR]

Abstract: BRICS (Brazil, Russia, India, China and South Africa) are viewed currently as pillars of relative political, economic and financial stability, with the prospect of a major shift in future world power. The paper aims at investigating the relationships among the economic, financial and political country risk ratings of the BRICS and relating those risk factors to their respective national stock markets in the presence of representatives of the world's major stock markets and oil market. It also examines the interrelationships among the national country financial risk ratings factors to discern transmission of the risk spectrum among the countries of this group because of the relevance of this information to investors, traders and policy makers. The results demonstrate that only the Chinese stock market is sensitive to all the factors. Financial risk ratings generally demonstrate more sensitivity than economic and political risk ratings, and political risk is sensitive to both financial and economic risk ratings. Among the five BRICS, Brazil shows special sensitivity to economic and financial risks, while Russia and China hold strong sensitivity to political risk and India demonstrates special sensitivity to higher oil prices. Among the global factors, oil price is more sensitive to economic than financial risk, while the S&P 500 reverses this relationship. The two American quantitative easings (QEs) affect BRICS differently. [Copyright &y& Elsevier]