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MODELLING SPREAD OF CORONA VIRUS USING ADAPTED BASS MODEL
Abstract
Forecasts for epidemics like COVID-19 are based on the epidemic compartmental model which characterizes the spread mechanism of infectious disease. While there are attempts to propose viral product diffusion models using epidemiological approaches, the attempt being made here is to use product diffusion model to forecast spread of COVID-19 epidemic in India.
... In a second paper [2], the authors showed that uneven distribution of population is a major cause of surges and waves of infection. In both studies, and in other studies as well [6], methods and models for prediction of size and duration of epidemics are based on OLS (Optimal Least Squares) curve fitting of an idealized mathematical model to actual data. This approach seems rather ad hoc compared to understanding the basic processes of infection. ...
... The macro-scale behavior can be modeled with nearly any logistics curve and OLS fitting. The Bass model will do, nicely [4,5,6,7]. But micro-scale models lack detail of the contagion network's structure. ...
A contagion network forms as a subnetwork within a larger "social network" when actors become infected and transmit infections to others. Nodes represent infected actors, and links represent contact that resulted in transmitting the infection from one person to another. The result of random contact is a non-random contagion network. Simulation of an SIR contagion shows emergence of a scale-free micro-scale structure with degree and betweenness distributions that obey a power law. Thus, contagion networks are the result of mild self-organization of scale-free structure-both degree distribution and betweenness centrality distribution obey a power law. This surprising result reinforces public health policies that advocate contact tracing and testing as early and fast as possible. An effective counter measure, barring availability of a vaccine, is testing and contact tracing back in time as far as possible, to disrupt the emergence of a contagion network.
... Buhat et al. (2020) developed a mathematical model of transmission of COVID-19 between health care providers and the general public. Gupta (2020) utilised an adapted bass model to project the spread of coronavirus in India. ...
... The irregularities of the curve indicate that the spread of the coronavirus is very intricate. Various factors play an amount of influence on the cause of the virus complexity (Azarafza et al., 2020;Gupta, 2020). Also, studies say that the disease is similar to the butterfly hypothesis, where the virus transmission can have a dynamo effect on other systems. ...
Understanding the spread of the COVID-19 pandemic is one of the most studied phenomena at present. Researchers were using various models to show their characteristics to make solutions. In this study, an adapted bass diffusion model was used to determine the time when the COVID-19 curve flattens in the Philippines. Further, it also determined the possible incidence of the second wave of infection. Also, it forecasted the number of infections per month and calculated the doubling time. Results revealed that the flattening of the curve is still not happening at present in the Philippines. The country is still facing the first wave. With this, sustaining and boosting its strategies in fighting the spread of the virus is a priority.
... Buhat et al. (2020) developed a mathematical model of transmission of COVID-19 between health care providers and the general public. Gupta (2020) utilised an adapted bass model to project the spread of coronavirus in India. ...
... The irregularities of the curve indicate that the spread of the coronavirus is very intricate. Various factors play an amount of influence on the cause of the virus complexity (Azarafza et al., 2020;Gupta, 2020). Also, studies say that the disease is similar to the butterfly hypothesis, where the virus transmission can have a dynamo effect on other systems. ...
Understanding the spread of the COVID-19 pandemic is one of the most studied phenomena at present. Researchers were using various models to show their characteristics to make solutions. In this study, an adapted bass diffusion model was used to determine the time when the COVID-19 curve flattens in the Philippines. Further, it also determined the possible incidence of the second wave of infection. Also, it forecasted the number of infections per month and calculated the doubling time. Results revealed that the flattening of the curve is still not happening at present in the Philippines. The country is still facing the first wave. With this, sustaining and boosting its strategies in fighting the spread of the virus is a priority.
... The first attempt to apply the Bass model to infectious disease was an extended model by Gupta [8]. He introduced an additional parameter called the outcome rate for forecasting the spread of the pandemic. ...
This article explores the ongoing COVID-19 pandemic, asking how long it might last. Focusing on Bahrain, which has a finite population of 1.7M, it aimed to predict the size and duration of the pandemic, which is key information for administering public health policy. We compare the predictions made by numerical solutions of variations of the Kermack-McKendrick SIR epidemic model and Tsallis-Tirnakli model with the curve-fitting solution of the Bass model of product adoption. The results reiterate the complex and difficult nature of estimating parameters, and how this can lead to initial predictions that are far from reality. The Tsallis-Tirnakli and Bass models yield more realistic results using data-driven approaches but greatly differ in their predictions. The study discusses possible sources for predictive inaccuracies, as identified during our predictions for Bahrain, the United States, and the world. We conclude that additional factors such as variations in social network structure, public health policy, and differences in population and population density are major sources of inaccuracies in estimating size and duration.
... In a second paper [2], the authors showed that uneven distribution of population is a major cause of surges and waves of infection. In both studies, and in other studies as well [3], methods and models for prediction of size and duration of epidemics are based on OLS (Optimal Least Squares) curve fitting of an idealized mathematical model to actual data. This approach seems rather ad hoc compared to understanding the basic processes of infection. ...
... The first attempt to apply the Bass model to infectious disease was an extended model by Gupta [8]. He introduced an additional parameter called the outcome rate for forecasting the spread of the pandemic. ...
In this paper we answer the questions how long will Covid-19 last in Bahrain with a finite population of 1.7M, and what is its final size? We compare the predictions made by numerical solutions of variations of the Kermack-McKendrick(KM) SIR Epidemic model and Tsallis-Tirnakli model with the curve fitting solution of the Bass model of product adoption. The results show that estimating parameters is a difficult task, which leads to initial predictions far from reality. The Tsallis-Tirnakli and Bass models yield more realistic results using data-driven approaches but greatly differ in their predictions. Finally, we identify possible sources of inaccuracies in predicting COVID-19 duration and size in Bahrain, the United States, and the world. We conclude that additional factors such as variations in social network structure, public health policy, and population are major causes of inaccuracies in estimating size and duration.
... For this purpose the Bass Model was adapted. (Gupta, 2020a); and this model does not try to mimic data from any other country. ...
Centres for Disease Control and Prevention of the United States (CDC) cites nine models on its website which are in use for modelling the current COVID-19 outbreak. Institutions in the UK and Singapore are adopting different models. An attempt has been made to use a product diffusion model, which is a non-epidemiology model, to forecast spread of COVID-19 epidemic in India. Models need recalibration as more data pours in. In this novel attempt to use the Adapted Bass model, parameters are re-estimated on a weekly basis. The changes in the model parameters are discussed in terms of their likely causes and probable implications. Forecasts for next seven weeks beginning 15 May based on current and previous estimates of model parameters are presented.
... For this purpose the Bass Model was adapted. (Gupta, 2020a); and this model does not try to mimic data from any other country. The basic Bass model is incredibly simple. ...
Modelling the current COVID-19 outbreak is much more challenging, simply because researchers know very little about the disease. Modelling based on data from Europe, China or the US makes little sense due to India’s unique social structures and approach to managing the public health. An attempt has been made to use product diffusion model, which is a non-epidemiology model, to forecast spread of COVID-19 epidemic in India. Since models need recalibration, model parameters are re-estimated on a weekly basis using the observed values relating to the spread of the disease. The changes in the model parameters are discussed in terms of their likely causes and probable implications. Forecasts for next six weeks beginning 08 May based on current and previous two estimates of model parameters are reported.
... For this purpose the Bass Model was adapted. (Gupta, 2020a). The basic Bass model is incredibly simple. ...
Modelling the current COVID-19 outbreak is much more challenging, simply because researchers know very little about the disease. An attempt has been made to use product diffusion model, which is a non-epidemiology model, to forecast spread of COVID-19 epidemic in India. Since models need re-calibration, the Adapted Bass model is being subjected to marginal calibration. In this calibration, model parameters are re-estimated on a weekly basis using the observed values relating to the spread of the disease. The new estimates, so obtained, are then used in forecasting the spread further on. The changes in the model parameters are discussed in terms of their likely causes and probable implications. Forecasts for seven weeks beginning 01 May based on current and previous two estimates of model parameters are reported.
... epidemiological approaches, an attempt was made to use product diffusion model to forecast spread of COVID-19 epidemic in India. (Gupta, 2020) An attempt was made to use product diffusion model to forecast spread of COVID-19 epidemic in India. For this purpose the Bass Model was adapted. ...
Forecasts for epidemics like COVID-19 are based on the epidemic compartmental model. An attempt has made to use product diffusion model to forecast spread of COVID-19 epidemic in India. Forecasting models can be subjected to Probabilistic calibration, exceedance calibration and marginal calibration. Marginal calibration concerns the equality of forecast situation and actual situation. Since very limited data is so far available, only marginal calibration can be attempted. The new estimates of parameters, so obtained, are then used in the model for forecasting from that point in time forward. This article reports the first weekly recalibration since the launch of the forecasting model.
Use of Bass product diffusion model in forecasting spread of COVID-19 epidemic in India was attempted. Forecasting Models need calibration on the basis of new observation data that flows in and marginal calibration concerns the equality of forecast and actual situation. The Adapted model is being subjected to marginal calibration. In this calibration, model parameters, p, q and o; are re-estimated on a weekly basis using the observed values of S(t), Y(t) and O(t). The new estimates, so obtained, are then used in the model for forecasting from that point onwards. This article reports the second weekly recalibration since the launch of the forecasting model. The changes in the model parameters have been discussed in terms of their causes and likely implications. Forecasts for the Five weeks during the Month of May based on the original parameters, first calibration and second calibration are reported.
To investigate the diffusion of products in the market, this paper proposes a viral product diffusion model using an epidemiological approach. This model presents the process of product diffusion through the dynamics of human behaviors. Based on the stability theory of Ordinary Differential Equations, we demonstrate the conditions under which a product in the market persists or dies out eventually. Next, we use Google data to validate the model. Fitting results illustrate that the viral product diffusion model not only depicts the steady growth process of products, but also describes the whole diffusion process during which the products increase at the initial stage and then gradually decrease and sometimes even exhibit multiple peaks. This shows that the viral product diffusion model can be used to forecast the developing tendency of products in the market through early behavior of these products. Moreover, our model also provides useful insights on how to design effective marketing strategies via social contagions.
Over a large number of new products and technological innovations, the Bass diffusion model (Bass 1969) describes the empirical adoption curve quite well. In this study, we generalize the Bass model to include decision variables such as price and advertising. The generalized model reduces to the Bass model as a special case and explains why the Bass model works so well without including decision variables. We compare our generalized Bass model to other approaches from the literature for including decision variables into diffusion models, and our results provide both theoretical and empirical support for the generalized Bass model. We also show how our generalized Bass model can be used for product planning purposes.
The paper that I authored and that was published in Management Science in 1969 (Bass 1969) has become widely known as the "Bass Model" (see Morrison and Raju 2004). The model of the diffusion of new products and technologies developed in the paper is one of the most widely applied models in management science. It was especially gratifying for me to learn that INFORMS members have voted the "Bass Model" paper as one of the Top 10 Most Influential Papers published in the 50-year history of Management Science in connection with the 50th anniversary of the journal. In this commentary on the paper I shall discuss some background and history of the development of the paper, the reasons why the model has been influential, some important extensions of the model, some examples of applications, and some examples of the frontiers of research involving the Bass Model. In the current period, in which there is much discussion about the marketing of applications of management science methods and practice, I hope that this commentary will be useful in providing insights about some of the properties of models that will be applied.
(This article originally appeared in Management Science, January 1969, Volume 15, Number 5, pp. 215–227, published by The Institute of Management Sciences.)
A growth model for the timing of initial purchase of new products is developed and tested empirically against data for eleven consumer durables. The basic assumption of the model is that the timing of a consumer's initial purchase is related to the number of previous buyers. A behavioral rationale for the model is offered in terms of innovative and imitative behavior. The model yields good predictions of the sales peak and the timing of the peak when applied to historical data. A long-range forecast is developed for the sales of color television sets.
Coronavirus: India defiant as millions struggle under lockdown
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