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In this paper, a new Susceptible-Exposed-Symptomatic Infectious-Asymptomatic Infectious-Quarantined-Hospitalized-Recovered-Dead (SEI_DI_UQHRD) deterministic compartmental model has been proposed and calibrated for interpreting the transmission dynamics of the novel coronavirus disease (COVID-19). The purpose of this study is to give a tentative prediction of the epidemic peak for Russia, Brazil, India and Bangladesh which could become the next COVID-19 hotspots in no time by using a Trust-region-reflective (TRR) algorithm which one of the well-known real data fitting techniques. Based on the publicly available epidemiological data from late January until 10 May, it has been estimated that the number of daily new symptomatic infectious cases for the above mentioned countries could reach the peak around the beginning of June with the peak size of  ∼ 15, 774 (95% CI, 12,814-16,734) symptomatic infectious cases in Russia,  ∼ 26, 449 (95% CI, 25,489-31,409) cases in Brazil,  ∼ 9, 504 (95% CI, 8,378-13,630) cases in India and  ∼ 2, 209 (95% CI, 2,078-2,840) cases in Bangladesh. As of May 11, 2020, incorporating the infectiousness capability of asymptomatic carriers, our analysis estimates the value of the basic reproduction number (R₀) as of May 11, 2020 was found to be  ∼ 4.234 (95% CI, 3.764-4.7) in Russia,  ∼ 5.347 (95% CI, 4.737-5.95) in Brazil,  ∼ 5.218 (95% CI, 4.56-5.81)in India,  ∼ 4.649 (95% CI, 4.17-5.12) in the United Kingdom and  ∼ 3.53 (95% CI, 3.12-3.94) in Bangladesh. Moreover, Latin hypercube sampling-partial rank correlation coefficient (LHS-PRCC) which is a global sensitivity analysis (GSA) method is applied to quantify the uncertainty of our model mechanisms, which elucidates that for Russia, the recovery rate of undetected asymptomatic carriers, the rate of getting home-quarantined or self-quarantined and the transition rate from quarantined class to susceptible class are the most influential parameters, whereas the rate of getting home-quarantined or self-quarantined and the inverse of the COVID-19 incubation period are highly sensitive parameters in Brazil, India, Bangladesh and the United Kingdom which could significantly affect the transmission dynamics of the novel coronavirus. Our analysis also suggests that relaxing social distancing restrictions too quickly could exacerbate the epidemic outbreak in the above-mentioned countries.

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A new mathematical model of chronic hepatitis C virus (HCV) infection incorporating humoral and cell-mediated immune responses, distinct cell proliferation rates for both uninfected and infected hepatocytes, and antiviral treatment all at once, is formulated and analysed meticulously. Analysis of the model elucidates the existence of multiple equilibrium states. Moreover, the model has a locally asymptotically stable disease-free equilibrium whenever the basic reproduction number is less than unity. Local sensitivity analysis (LSA) result exhibits that the most influential (negatively sensitive) parameters on the epidemic threshold are the drug efficacy of blocking virus production and the drug efficacy of removing infection. However, LSA does not accurately assess uncertainty and sensitivity in the system and may mislead us since by default this technique holds all other parameters fixed at baseline values. To overcome this pitfall, one of the most robust and efficient global sensitivity analysis (GSA) methods which is Latin hypercube sampling-partial rank correlation coefficient technique elucidates that the proliferation rate of infected hepatocytes and the drug efficacy of killing infected hepatocytes are highly sensitive parameters that affect the transmission dynamics of HCV in any population. Our study suggests that cell proliferation of the infected hepatocytes can be very crucial in controlling disease outbreak. Thus, a future HCV drug that boosts cell-mediated immune response is expected to be quite effective in controlling disease outbreak.

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Volatility is the most important concept in options trading. No one can consistently predict the market, not even the experts. Yet many investors think they can guess what will happen, based on hunches or rumors. Unless we know precisely when to buy or sell, we can, and probably will miss the market. This can really cost us. Most of the market’s gain and loss occur in just a few, but unpredictable, trading days. In this paper we study the differences in unpredictability of stock and option prices using Black and Scholes model and EWMA volatility model. This difference eventually affects options range and premiums.