Although policy makers recommend or impose various standard measures, such as social distancing, movement restrictions, wearing face masks and washing hands, against the spread of the SARS-CoV-2 pandemic, individuals follow these measures with varying degrees of meticulousness, as the perceptions regarding the impending danger and the efficacy of the measures are not uniform within a population. In this paper, a compartmental mathematical model is presented that takes into account the importance of personal cautiousness (as evidenced, for example, by personal hygiene habits and carefully following the rules) during the COVID-19 pandemic. Two countries, Turkey and Italy, are studied in detail, as they share certain social commonalities by their Mediterranean cultural codes. A mathematical analysis of the model is performed to find the equilibria and their local stability, focusing on the transmission parameters and investigating the sensitivity with respect to the parameters. Focusing on the (assumed) viral exposure rate, possible scenarios for the spread of COVID-19 are examined by varying the viral exposure of incautious people to the environment. The presented results emphasize and quantify the importance of personal cautiousness in the spread of the disease.

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We present a mathematical model for a market involving two stocks which are traded within a single homogeneous group of investors who have similar motivations and strategies for trading. It is assumed that the market consists of a fixed amount of cash and stocks (additions in time are not allowed, so the system is closed) and that the trading group is affected by trend and valuation motivations while selling or buying each asset, but follows a strategy in which the buying of an asset depends on the other asset's price while the selling does not. By utilizing these assumptions and basic microeconomics principles, the mathematical model is obtained through a dynamical system approach. We analyze the stability of equilibrium points of the model and determine the conditions on parameters for stability. First, we prove that all equilibria are stable in the absence of a clear emphasis on a trendbased value for each stock. Second, for systems in which the group of traders attaches importance to the valuation of one stock and the trend of the other stock for trading, we establish conditions for stability and show with numerical examples that when instability occurs, it is exhibited by oscillations in the price of both stocks. Moreover, we argue the existence of periodic solutions through a Hopf bifurcation by choosing the momentum coefficient as a bifurcation parameter within this setting. Finally, we give examples and numerical simulations to support and extend the analytical results. One of the key conclusions for economics and finance is the existence of a cyclic behavior in the absence of exogenous factors according to the momentum coefficient. In particular, an equilibrium price that is stable becomes unstable as the trend based trading increases. Published under license by AIP Publishing. https:/ /doi.ARTICLE scitation.org/journal/cha that are routinely examined by practitioners. Stability analyses and numerical studies imply that equilibrium prices are stable if the group of investors focuses on only the fundamental values of the assets being traded. In contrast, trading that is largely affected by momentum effects leads to instabilities in the asset prices, which are characteristics of the crises of financial markets such as the high-tech bubble of 1998-2000 in the United States. Another important result is the possibility of the existence of periodic solutions that are not permitted in classical finance theory.