Estimating the Number of COVID-19 Cases and Impact of New COVID-19 Variants and Vaccination on the Population in Kerman, Iran: A Mathematical Modeling Study.

COVID-19 is spreading all over Iran, and Kerman is one of the most affected cities. We conducted this study to predict COVID-19-related deaths, hospitalization, and infected cases under different scenarios (scenarios A, B, and C) by 31 December 2021 in Kerman. We also aimed to assess the impact of new COVID-19 variants and vaccination on the total number of COVID-19 cases, deaths, and hospitalizations (scenarios D, E, and F) using the modified susceptible-exposed-infected-removed (SEIR) model. We calibrated the model using deaths reported from the start of the epidemic to August 30, 2021. A Monte Carlo Markov Chain (MCMC) uncertainty analysis was used to estimate 95% uncertainty intervals (UI). We also calculated the time-varying reproductive number (R t) following time-dependent methods. Under the worst-case scenario (scenario A; contact rate = 10, self-isolation rate = 30%, and average vaccination shots per day = 5,000), the total number of infections by December 31, 2021, would be 1,625,000 (95% UI: 1,112,000-1,898,000) with 6,700 deaths (95% UI: 5,200-8,700). With the presence of alpha and delta variants without vaccine (scenario D), the total number of infected cases and the death toll were estimated to be 957,000 (95% UI: 208,000-1,463,000) and 4,500 (95% UI: 1,500-7,000), respectively. If 70% of the population were vaccinated when the alpha variant was dominant (scenario E), the total number of infected cases and deaths would be 608,000 (95% UI: 122,000-743,000) and 2,700 (95% UI: 700-4,000), respectively. The R t was ≥1 almost every day during the epidemic. Our results suggest that policymakers should concentrate on improving vaccination and interventions, such as reducing social contacts, stricter limitations for gathering, public education to promote social distancing, incensing case finding and contact tracing, effective isolation, and quarantine to prevent more COVID-19 cases, hospitalizations, and deaths in Kerman.

A new method for rooting nonlinear equations based on the Bisection method.

Finding the roots of nonlinear equations has many applications in various sciences, especially engineering, and various methods have been proposed for this purpose. However, almost all these methods have some shortcoming. This paper presents a new method, where we consider the desired function to find the root(s) of the absolute value, so the root(s) (if any) is the absolute minimum. Using Monte Carlo method, we divide the desired distance into smaller parts. In each section where the slope of the function changes, we use the Bisection method to find the root. It largely covers the limitations of previous methods. The most important advantage of this method over the Bisection method is that it finds all the roots of the equation.•Solve the problem of the bisection method in roots tangent to the x-axis.•Separation of Root(s) that crossed and Root(s) that are tangent to the x-axis.

A method for estimating width bands of variables in economics under uncertainty conditions.

This study develops a method to estimate the width bands of variables in economics by fuzzy logic. One of its important features is flexibility in the conditions of economic uncertainty, which can be used to model the uncertainty of external and internal factors on economic variables. In this study, for example, the effect of uncertainty of external factors on the Gini coefficient (income distribution) is investigated. For this purpose, we use the fuzzy logistic smooth transition autoregressive (FLSTAR) model and the Gini coefficient is estimated in three bounds (high, middle and low). The result of this estimation suggest that by appropriate policy making the Gini coefficient can be decreased to the lower bound. Another results of this study is that the authorities should prevent the increase of the Gini coefficient in the middle and upper bands with proper planning for the future. In brief,•This study introduces a novel method for estimating high, low and middle bounds of economic variables under uncertainty conditions.•One practical results of this method is to compare high, medium, and low bands of the variables with their current trends, which is a benchmark for policymaking and evaluating the effectiveness of government's policies.•Programs designed with this method are fast and have low cost.

Estimation of upper and lower bounds of Gini coefficient by fuzzy data.

The data presented in this paper are used to examine the uncertainty in macroeconomic variables and their impact on the Gini coefficient. Annual data for the period 2017 - 1996 are taken from the Bank of Iran website https://www.cbi.ir. We used fuzzy regression with symmetric coefficients to calculate upper and lower bound data of Gini coefficient. Estimated data at this stage can be a very useful guide for policymakers, on the other hand, it is a benchmark for evaluating the effectiveness of government policies. The reason for using fuzzy regression to estimate data on Gini coefficients is the extra flexibility of this model.