4 min read.Updated: 12 Aug 2020, 06:08 PM ISTAnandadeep Mandal,Neelam Rani
Robust model estimations that include maximum likelihood Bayesian interference methods take into consideration the uncertainty of the data sources by allowing the data at each point to follow a probabilistic distribution
Since the outbreak of covid-19, several variants of deterministic epidemic models have been used to study the propagation of the infectious disease.
As governments across the globe seek to effectively respond to contain the spread of the virus, it is essential that modelers estimate the severity of the epidemic in terms of: i) total number of infected, ii) total number of confirmed cases, iii) number of deaths iv) the course of its peak, v) reproduction rate and vi) total duration of the pandemics.
Among the models used, SIR (susceptible, infectious, or recovered) and SEIR (susceptible, exposed, infectious, or recovered) models are the most common. However, the models have shown a wide range of variations across all nations. Considering India, the estimated basic reproduction number (R0) varied from 2.1 to 3.35 in May and to 1.67 to 2.45 during the first week of August. The peak times estimated varied from May to August , and now it is estimated to be by September. Why is there such a wide variation when using deterministic epidemic transmission models in specific months and the peak have been miscaliberated? Here, we highlight the key concerns in using such models as a standard framework.
The initial issues for the wide range of model predictions can be related to the lack of information. Till the middle of February, there was too little information of confirmed cases. This was a major concern and the reliability of data was an additional issue. However, robust model estimations that include maximum likelihood Bayesian interference methods take into consideration the uncertainty of the data sources by allowing the data at each point to follow a probabilistic distribution. This implies that the lack of data has been a more serious concern.
The key issue that explains the variability of the model predictions is understanding how confirmed cases compare with the model forecasts. Confirmed cases are people who are infected and have made contact with the hospital and whose infection has been tested positive. In contrast, the ‘infected compartment’ in the transmission models include people those who have shown symptoms and have been tested and also those who may or may not have symptoms and have not been tested. The ratio of the cumulative confirmed cases to the cumulative infected people is the case-infection ratio. But, why is this an issue for modelling the covid-19 transmission in India? In model calibration for estimating transmission rate, it is necessary to discount the total number of infectious people by the case-infection-ratio to determine the reproduction number (R0), the scale of the epidemic, as well as the peak time. Thus, if testing is not carried out at an optimum desired level, the model predictions are misspecified. Increasing testing for covid-19 is, therefore, critical.
There are other two concerns. These relate to the models used and the way they are estimated. Given confirmed-case data, there is a linkage between the model parameters and the transmission rate. Different combination of these parameters can yield different model predictions. This is known as non-identifiability of the model. The way in which this issue is addressed significantly influences the reliability and the predictability of the models. Standard non-linear models fail to address this issue. The other factor that significantly affects the model predictions is the choice of the model itself. Choice of a suitable model to describe the epidemic is critical. In a complex model, several biological and epidemiological information are considered that makes the estimation more biologically realistic. However, in a complex model, the number of parameters to be estimated is much larger than a simple model. Many such parameters are unknown, given the confirmed cases of covid-19. Thus, it increases the degree of uncertainty in model output. Therefore, in choosing an appropriate model, it is important to have a balanced approach between biological realism and reducing uncertainties in the model predictions.
Thus, the existing deterministic SIR/SEIR models should be estimated with precaution. A stable model that predicts the course of the epidemic is required under these conditions. A more accurate model would be an extension of the classical SIR model for human-to-human transmission.
The following eight key stages of infection may be considered i) suspected, ii) infected, iii) diagnosed, iv) ailing, v) cured, vi) re-infected, vii) vulnerable, and viii) dead. It is important that the model distinguishes between diagnosed and non-diagnosed individuals as the former may responsibly isolate and reduces the spread of infection. Further, the reproduction number of covid-19 transmission should be differentiated in order to capture the varying healthcare facilities and the impact of the lockdown measures across different states and geographical provinces of India.
(Dr. Anandadeep Mandal is an assistant professor in Finance at the University of Birmingham, UK. Dr. Neelam Rani is an associate professor in the area of Finance at IIM Shillong. The views expressed in this column are their own and do not reflect Mint's.)