Improved SIR - Covid-19 Prediction Model

SIR (Susceptible-Infected-Removed) model to estimate the peak while a data-driven approach based on past outbreaks is used to predict the decline of the epidemic.

Covid - 19 Reports

Slowing down of the second wave of COVID-19 in India

May 24, 2021

Profs. Rajesh Ranjan and Mahendra Verma, along with their team at #IITKanpur, are working to provide model forecasts up to district-wise granularity. They have launched a website ( ) for updated daily forecasts.

Model observations:

  1. India infection has peaked in the first week of May and is currently on steep decline except for a few states. The average count of daily cases has become nearly 60% of its value on May 8, 2021, due to interventions.
  2. Test positivity rate (TPR) has also reduced from a very high value of about 23% on May 8, 2021, to about 12% due to increased daily testing capacity.
  3. Case fatality rate (CFR) has increased to nearly 1.7% but is expected to go down soon with decrease inactive infections.
  4. High TPR (>20%): Goa, Karnataka, Kerala, West Bengal, Tamilnadu, Odisha, Northeast states.
  5. Low TPR (<10%): UP, Delhi, Gujarat, Bihar, Jharkhand, Maharashtra, MP, Chhatisgarh, J&K, Punjab, Telangana, Uttarakhand.
  6. Lowest CFRs: Odisha (0.2%), Kerala (0.5%). Highest CFRs: Delhi (8%), Maharashtra (3.7%)
  7. States yet to saturate: West Bengal, Odisha, All-Northeast states

Second wave of COVID-19 in India

May 09, 2021

Rajesh Ranjan and Mahendra Verma, IIT Kanpur

India is overwhelmed by the second wave with more than 37 lacs active cases.  Because of over-stretched healthcare systems, the case fatality rate (CFR) has also increased from about 0.7% in February to about 1%.  However, it is still lower than several other countries including Brazil, Russia, and France. We have used Susceptible-Infected-Recovered (SIR) model along with a data-driven decay rate to predict the future course of the pandemic.

Our observations are as given below. Our daily-case forecasts using a model are shown as red curves in the figures.  The shaded regions are the uncertainties in the predictions.

  1. The model suggests that India is hovering around the peak, however, the peak caseload of about 4 lacs is limited by the daily testing capacity. Due to a very high test positivity rate (TPR) of approximately 22%, it is expected that India will see a near plateau for around a week instead of a sharp peak. In addition, the subsequent decay will also be slow (Figure 1).
  2. Maharashtra, Uttar Pradesh, Madhya Pradesh, Gujarat, Delhi, and Chattishgarh are exhibiting clear signs of decline indicating that lockdown has an impact in arresting the spread (Figure 2). The model suggests that in recent times, daily cases have reached their peaks in Kerala, Haryana, Rajasthan, Telangana, Bihar, and Jharkhand, but there are strong fluctuations in the data (Figure 3). However, considering the high infectiousness of the virus, strict vigilance is a must even in regions exhibiting decline. We should not make the same mistake as in the near past.
  3. Karnataka and Andhra Pradesh are expected to peak soon, while Tamilnadu may peak in the third week of May (Figure 4). Uttarakhand, Punjab, West Bengal, Odisha, Puducherry, Chandigarh, Goa, J&K are still in the growth phase and may take a couple of more weeks to the peak. We believe that strong measures are needed in these states to suppress explosive growth.
  4. Virus spread is now moving from North India to Eastern and Northeast states. West Bengal, Assam, Mizoram, Meghalaya, Manipur, and Sikkim are behind other states in terms of overall spread and saturation. Therefore, it is possible to curb the growth now through strong intervention before the situation becomes worse.
  5. Goa has the highest TPR of about 50% suggesting a very high spread of the virus. Uttarakhand, Karnataka, West Bengal, Kerala, and Haryana too have a very high TPR of approximately 30%. Testing capacity needs to be ramped in these states while continuing interventions to effectively contain the spread of the epidemic.
  6. Among the most impacted states, Kerala has the lowest CFR of just about 0.14% suggesting quality health infrastructure. Jharkhand (2.2%), Punjab (2%) and Delhi (1.7%) have very high CFR, which is a cause of concern.

Research Link:

Grim situation of COVID-19's Second Wave

April 18, 2021

Rajesh Ranjan, Aryan Sharma, and Mahendra Verma, IIT Kanpur

Strong second wave of COVID-19 is creating a havoc in the country.  As on 17th April, the infection count is 2.66 lacs, while the death count is about 1500.  Although the vaccination drive is expanded gradually to include all age groups, the spread of the highly infectious new mutant of the pathogen (B.1.617 lineage, UK and SA variants) poses a major health emergency.

We have analyzed the data up to 15th April 2021 and observed dangerous trends. See  Our key findings are listed below:

  1. The pandemic has spread intensely across all states, as is evident from the effective reproduction number Rt shown in Figure 1 and Table 1. Major disconcerting issue is Rt being close to 2 in some of the populous states, such as Uttar Pradesh, Bihar, and West Bengal.
  2. The exponential growth rate for the second wave is more than double of the first wave. This is the reason for dramatic increase in numbers.  The alarming issue is that we are on the rapid growth phase for the last four weeks (see Figure 2).
  3. Based on preliminary analysis using the available data and the SIR model, we forecast the second wave to peak in mid-May with the daily infection count exceeding 3.5 lacs.
  4. The current Case Fatality Rate (CFR) for the country is approximately 1.2%. However, with the dramatic increase in the infection count, the healthcare is going to be overstretched and therefore can cause an increase in CFR.
  5. Data shows that the second wave has reached the rural area. This could cause devastation considering poor healthcare infrastructure in these regions.

The above observations suggest that the flattening of the second wave requires strong administrative intervention and people’s participation.

Figure 1: Variations in daily counts (incidences) and Rt in most-impacted states

Figure 2: Comparison of first and second wave

Table 1: Statewise characterization of second wave as on April 15, 2021.

Test Positivity Rate (TPR), Case Fatality Rate (CFR), Rt, Vaccinations per 100 persons (at least one dose)

Second wave of COVID-19 in India

March 27, 2021

Rajesh Ranjan, Aryan Sharma, and Mahendra Verma; IIT Kanpur

India is exhibiting signs of a second wave of COVID-19 as already seen in the United States and several other European countries including France and the United Kingdom. Although the vaccination drive is expanded gradually to include all age groups, the emergence of several new mutants of the pathogen, which are highly transmissible, poses a health emergency situation. We have plotted the variation in basic Reproduction number, R, with time to understand the emerging dynamics of COVID-19 spread in key states and India as a whole.

  1. Since late Feb 2021, the value of R is consistently above 1 clearly indicating a second wave. For nearly 5 months between Oct 2020 and Feb 2021, R stayed below 1 where the pandemic was showing signs of decline. Relatively late arrival of the second wave in India, compared to those in several other countries in the world, could be due to the recent spread of more contagious mutants, although they are less virulent.
  2. R-value on 27 March 2021 is approximately 1.26, which is very close to the value in early May 2020. Therefore, following the trend from the first wave, it may be estimated that the number of active cases is going to rise for the next 3-4 months unless the social distancing norms are strictly enforced, and vaccination efforts are expedited.
  3. The second wave has an exponential growth with exponents bigger than the first one. Further, since the daily new cases (about 60,000) are already at the level of August 2020, it is expected that with the current growth trend the second peak will be higher than the first one.
  4. Although Maharashtra contributes to nearly 70% of the daily new cases in the second wave, the rapid growth of cases in several other states such as Punjab, Haryana, Gujarat, Madhya Pradesh, Uttar Pradesh show reproduction number close to the national trend. These states may be a month behind Maharashtra and therefore it is necessary to curb this rise through strict social distancing practices with higher compliance as in the first phase.