The Basic reproduction number is the average number of secondary infection cases generated by a single primary case in a susceptible population. Estimation of the Basic reproduction number is important in medical studies. In this paper, we describe a new method for estimating the Basic reproduction number by branching processes. Finally, we apply this estimator on real data reported by the National Center for Biotechnology Information in the USA.

In the nineteenth century recurrent epidemics of cholera and influenza and decreasing cases of diseases in later years produced the question why communicable disease would suddenly produce epidemics and then disappear.Designing one model bases mathematically such as SIR model has been done for the question response. The aim of research survey model has been done on the measles in Iran and determination of outbreaks of measles at 1996 to determine the least vaccine covering for prediction of measles epidemics in the future.With collection of data from disease control centers, the number of suffering with measles, age mean of measles and life expanse was calculated and the amount of R0(Basic reproduction Rate) resulted. Calculating R0 amount at range 5.5 to 7.49 for the reason R0 resulted in amounts greater than the measles epidemic that occurred in our country and least effective vaccine was 81.8-86.65%. Calculating R0 and the least vaccine predicted for measles epidemics determined that epidemic control vaccine must be more than 82.65% to decrease herd immunity and increase measles age mean under conditions due to another epidemic in the 2005.

Background: Estimation of the Basic reproduction number of an infectious disease is an important issue for controlling the infection. Here, we aimed to estimate the Basic reproduction number (0) of COVID-19 in Iran. Methods: To estimate 0 in Iran and Tehran, the capital, we used 3 different methods: exponential growth rate, maximum likelihood, and Bayesian time-dependent. Daily number of confirmed cases and serial intervals with a mean of 4. 27 days and a standard deviation of 3. 44 days with gamma distribution were used. Sensitivity analysis was performed to show the importance of generation time in estimating 0. Results: The epidemic was in its exponential growth 11 days after the beginning of the epidemic (Feb 19, 2020) with doubling time of 1. 74 (CI: 1. 58-1. 93) days in Iran and 1. 83 (CI: 1. 39-2. 71) in Tehran. Nationwide, the value of 0 from February 19 to 29 using exponential growth method, maximum likelihood, and Bayesian time-dependent methods was 4. 70 (95% CI: 4. 23-5. 23), 3. 90 (95% CI: 3. 47-4. 36), and 3. 23 (95% CI: 2. 94-3. 51), respectively. In addition, in Tehran, 0 was 5. 14 (95% CI: 4. 15-6. 37), 4. 20 (95% CI: 3. 385. 14), and 3. 94 (95% CI: 3. 45-4. 40) for exponential growth, maximum likelihood, and Bayesian time-dependent methods, respectively. Bayesian time dependent methods usually provide less biased estimates. The results of sensitivity analyses demonstrated that changes in the mean generation time affect estimates of 0. Conclusion: The estimate of 0 for the COVID-19 ranged from 3. 94 to 5. 14 in Tehran and from 3. 23 to 4. 70 in nationwide using different methods, which were significantly larger than 1, indicating the potential of COVID-19 to cause an outbreak.

After the onset of the COVID-19 outbreak in Wuhan, China, and its spread to other countries, confrontation with it as an international emergency in all countries was seriously on the agenda of governments. Our country was not immune to this outbreak. Effective measures to combat this new virus would be certainly based on a proper understanding of the epidemiological pattern and its evaluation in the community. Under these circumstances, proper understanding and use of epidemiology-based indicators or approaches are more than ever needed by authorities and decision-makers. One of the most important and commonly used indices that have been used in most epidemics, including the COVID-19 outbreak, is the Basic reproduction number (R_0). Given the increasing need for the medical community and health care staff to deepen their understanding of the epidemiological concepts in dealing with epidemics, this article aimed to define R_0 and its application in the evaluation and monitoring of the COVID19 epidemiological pattern in society.

Background: Determining the epidemic threshold parameter helps health providers calculate the coverage while guiding them in planning the process of vaccination strategy. Since the trend and mechanism of influenza is very similar in different countries, we planned a study with the mentioned goal by using data of US from 2017 to 2018. Study design: A secondary study. Methods: R0 and corresponding vaccination coverage are estimated using the national and state-level data of the US from the 40th in 2017 to the 5th week in 2018. Four methods maximum likelihood (ML), exponential growth (EG), time-dependent reproduction numbers (TD), and sequential Bayesian (SB) are used to calculate minimum vaccination coverage. The gamma distribution is considered as the distribution and the generation of time. Results: The peak of epidemy in most states has occurred in the 15th week after the beginning of the epidemics. The generation time obey the Gamma distribution with mean and standard deviation of 3. 6 and 1. 6, respectively, was utilized for the generation time. The R0 (vaccination coverage) equaled 1. 94 (48. 4%), 1. 80 (44. 4%), 3. 06 (67. 3%), and 2. 11 (52. 6%) for EG, ML, SB, and TD methods at the national level, respectively. Conclusion: The R0 estimations were in the range of 1. 8-3. 06, indicating that an epidemic has occurred in the US (R0>1). Thus, it is required to vaccinate at least 44. 4% to 67. 3% to prevent the next epidemics of influenza. The findings of this study assist futures studies to apply disease control by vaccination strategies in order to prevent a national disaster.