key: cord-0966370-ne9nvydh authors: Yadav, Subhash Kumar; Akhter, Yusuf title: Response: Commentary: Statistical Modeling for the Prediction of Infectious Disease Dissemination With Special Reference to COVID-19 Spread date: 2022-01-31 journal: Front Public Health DOI: 10.3389/fpubh.2021.783201 sha: 6f6af0c60d07447f423ad83ae8e4758d09367324 doc_id: 966370 cord_uid: ne9nvydh nan With reference to the quoted commentary (1) above, commentators observed, "In sections 'SI and SIS Models' and . . . . chance or probability. " We would like to state that the commentators have misunderstood and misinterpreted the concept and definition of β. From the mentioned models, it may be seen that, β is the per capita per unit time infection rate. It is a disease transmission coefficient or a transmission rate as described by Kirkeby et al. (2). Bailey (3), at page no. 20, and Bailey (4), at page no. 33, have defined β as the infection rate. Chalub and Souza (5) have defined that, β may be interpreted as a rate or as a probability among many other possible choices. Jagan et al. (6) have defined β as the transmission rate; it is the number of infections per unit time per susceptible per infected. Further, Citron et al. (7) have defined as β the transmission rate, published in "PNAS" and others (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) . Further, we have mentioned that β estimates the spread rate, which shows the chance of transmission of the disease from an infectious individual to a susceptible one. Ucakan et al. (17) have explicitly expressed that the transmission coefficient, β estimates the probability of getting the disease from an infectious individual to the susceptible and stated it as a probability that ranges from 0 to 1 (0< β <1). On the other hand, Brauer and Castillo-Chavez (21) have defined β as the product of the probability of the transmission per contact and the per capita contact rate. In addition, Chen (22) has also defined β as the infection coefficient, the product of the average number of contacts within a given time period and the probability of infection for the contact between susceptible and infectious individuals. Thus, β may take a value >1 and, therefore, in general, it may not be considered as a probability. Furthermore, one should be very careful about the choice of β while defining diagrams for different epidemiological models. Moreover, Hethcote and Driessche (10) mentioned that the number of new cases per unit time shall be λSI/N, which is called the standard incidence (23) (24) (25) (26) (27) with λ as a contact rate. Another common incidence is the simple mass action incidence, βSI, where β was defined as the transmission coefficient (4, 9). Additionally, Okabe and Shudo (16) have defined that βSI represents the number of susceptible individuals that get infected per day. For more details, further references can be consulted (28, 29) . In their next comment, they have wrongly pointed out "In section, "The Distribution Fitting," the . . . . biological interpretations." In the section "The Distribution Fitting" of our review on page no. 04, we have clearly mentioned that "it is the growth rate of infection which determines the total number of infections which depends on the numerous factors (30) , " and in the context of distribution fitting, we have mentioned that the infectious disease mainly depends on two factors, namely, the number of carriers and the time of infection as reported by Datta et al. (31) . They have further mentioned, "In the section of "The Basic Reproduction Number". . . . . . not the model." In the section "The Basic Reproduction Number, " the commentators have wrongly stated the concept here. From the formula, it may be observed that, R 0 does not depend on time. Further, we have not mentioned R 0 as a rate anywhere in the review article. It is solely their imaginary creation. We have mentioned in the section that, R 0 is measured through the effective reproductive rate, denoted by R. Thus, we have mentioned, "effective reproductive number" R as "effective reproductive rate" since it depends on time (32) (33) (34) (35) (36) (37) (38) . Although for minimizing the ambiguity, the use of consistent terminology throughout the literature is required, and, therefore, we appreciate the commentators. Further, commentators have wrongly mentioned that we have stated ξ as a model in the sub-section SIRS on page no. 9, however, ξ is defined in subsection SEIRS on page no. 20. In our opinion, the sentence should be started with the word "In, " which may be a typographical error, however, we have clearly mentioned that ξ is the rate by which the recovered individuals become susceptible because of the loss of immunity, and ξ is not a model. For more details, further references can be referred to (15, 39, 40) . In their last comment, they have pointed out, "In the section, "Further Suggestions and Future Prospectives", . . . .. recommendations." Hajian-Tilaki (41) clearly observed that in designing epidemiologic studies, sample size calculation has an important role to detect an effect and achieve the desired precision in estimates of parameters of the interest (41) (42) (43) (44) (45) . Therefore, it is a key factor that must be considered while designing the study protocol (45) . Small sample size will fail to provide a precise estimate and reliable answers to the policy makers (46) . On the other hand, a large sample size than required will cause wastage of useful resources earmarked to the study (45) . Malhorta and Indrayan (47) have recorded that, an adequate estimation of the correct required sample size is a must, especially in the case of such infectious diseases, for which the newly invented diagnostic tests are expensive to carry out. For any epidemiological study, the investigators must present the principles of sample size calculation to justify these numbers (44) . Further, Hajian-Tilaki (48) also mentioned that, unfortunately, sample size calculations are rarely reported by clinical investigators for diagnostic studies (49, 50) . The sample size calculation may be ignored wherever required, for instance, assumptions in household epidemic models for determining the transmissibility (R 0 ). This can sometimes be seen based on who infected whom however, it is only applicable to the infections with a long incubation period, such as AIDS and tuberculosis. Although, for the infections with a shorter incubation period, such as Influenza and COVID-19, we must meet the sample size conditions in order to estimate the growth rate. The commentators mentioned that in the section "Further Suggestions and Future Prospective, " the compulsion of sample size determination can be avoided, however, we opined that, if certain researchers have not mentioned the assumptions regarding the sample size calculation, it does not mean that there is no need of it. Many a time, the determination of sample size is ignored, where strict ethical issues are not concerned, but it will harm in some sense or another, as mentioned by the more pragmatic scholars earlier (45, 46) . Thus, it is highly recommended for an epidemiological study that the appropriate sample size calculation should be followed (41, 48, (51) (52) (53) (54) (55) (56) (57) (58) A Model for the Spread of an SIS Epidemic in a Human Population. A thesis submitted for the degree of Doctor of Philosophy Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations On a network SIS model with opinion dynamics Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy A mathematical model of epidemics-a tutorial for students Analysing of tuberculosis in turkey through SIR, SEIR and BSEIR mathematical models Application of optimal control of infectious diseases in a model-free scenario Covid-19 sir model with nonlinear incidence rate An SIR-type epidemiological model that integrates social distancing as a dynamic law based on point prevalence and socio-behavioral factors Basic models in epidemiology Analyzing and Modeling Spatial and Temporal Dynamics of Infectious Diseases, 1st Edn Qualitative analysis of communicable disease models A thousand and one epidemic models Epidemiological models with heterogeneous populations: proportionate mixing, parameter estimation and immunization programs Dynamic models of infectious diseases as regulators of population sizes Disease transmission models with density-dependent demographics Estimating clinical severity of COVID-19 from the transmission dynamics in Wuhan, China SARS-CoV-2 viral load in upper respiratory specimens of infected patients Mathematical model of infection kinetics and its analysis for COVID-19, SARS and MERS infection, genetics and evolution Statistical modeling of COVID-19 pandemic stages worldwide Effective reproductive number estimation for initial stage of COVID-19 pandemic in Latin American Countries Public health measures and the reproduction number of SARS-CoV-2 Reproduction number (R) and growth rate (r) of the COVID-19 epidemic in the UK: methods of estimation, data sources, causes of heterogeneity, and use as a guide in policy formulation Predicting the SARS-CoV-2 effective reproduction number using bulk contact data from mobile phones Tracking R of COVID-19: a new real-time estimation using the Kalman filter Estimation of the reproduction number of influenza A(H1N1)pdm09 in South Korea using heterogeneous models Cost effective reproduction number based strategies for reducing deaths from COVID-19 Early dynamics of transmission and control of COVID-19: a mathematical modelling study Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes Sample size estimation in epidemiologic studies When was a negative clinical trial big enough? How many patients you needed depends on what you found Statistical power and sample size estimation for headache research: an overview and power calculation tools Statistical power and estimation of the number of required subjects for a study based on the t-test Sample size calculation and power analysis: a quick review An introduction to power and sample size estimation A simple nomogram for sample size for estimating sensitivity and specificity of medical tests Sample size estimation in diagnostic test studies of biomedical informatics Sample size of studies on diagnostic accuracy: literature survey Sample size in studies on diagnostic accuracy in ophthalmology: a literature survey Practical sample size calculations for surveillance and diagnostic investigations Improving the Sample Size Calculation Process for Peel Health: A Rapid Review of the Evidence. Region of Peel for You Sample Size Determination for Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease Sample size calculation for estimating key epidemiological parameters using serological data and mathematical modeling Sample size estimation in clinical research from randomized controlled trials to observational studies Sample size estimation in veterinary epidemiologic research Sample size calculation for phylogenetic case linkage The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.Publisher's Note: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.Copyright © 2022 Yadav and Akhter. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.