*[Submitted on 19 Nov 2020] ***A Generalized Epidemiological Model for COVID-19 with Dynamic and Asymptomatic Population**

Anirban Ghatak, Shivshanker Singh Patel, Soham Bonnerjee, Subhrajyoty Roy

**Abstract**

In this paper, we develop an extension of standard epidemiological models, suitable for COVID-19. This extension incorporates the transmission due to pre-symptomatic or asymptomatic carriers of the virus. Furthermore, this model also captures the spread of the disease due to the movement of people to/from different administrative boundaries within a country. The model describes the probabilistic rise in the number of confirmed cases due to the concomitant effects of (incipient) human transmission and multiple compartments. The associated parameters in the model can help architect the public health policy and operational management of the pandemic. For instance, this model demonstrates that increasing the testing for symptomatic patients does not have any major effect on the progression of the pandemic, but testing rate of the asymptomatic population has an extremely crucial role to play. The model is executed using the data obtained for the state of Chhattisgarh in the Republic of India. The model is shown to have significantly better predictive capability than the other epidemiological models. This model can be readily applied to any administrative boundary (state or country). Moreover, this model can be applied for any other epidemic as well.

Download**COVID-19 in India: Policy Suggestions using Epidemiological Modeling**

Anirban Ghatak^{a,1,1}, Ranraj Singh^{b}

^{a}*Formerly of Indian Institute of Management Visakhapatnam*

* ^{b}Indian Institute of Technology Dhanbad*

**Abstract**

In this policy paper, we implement a compartment based epidemiological model that incorporates control measures such as *Lockdown *and *Social Distancing *for the top fifteen most affected states in India using data upto 3rd May, 2020. We estimate the time varying effects of these control measures on the transmission rate of Covid-19 directly from the data. We predict the disease progression using the eSIR model for nine scenarios with different possible dates of lockdown relaxation followed by different levels of social distancing guidelines adopted post lockdown. Using the results of the simulations, we propose possible exit strategies for each state depending on factors such as the fraction of the population that will be infected at the peak and the hospital bed capacity.

*Keywords: *Epidemiology, SIR Model, COVID-19

**1. Introduction**

“All models are wrong but some are

useful.”

*George E. P. Box*

The Coronavirus Disease or COVID-19 had been declared a pandemic by the World Health Organisation. It is a highly infectious disease caused by the Novel Coronavirus SARS-CoV-2 for which no vaccine has been developed yet. This disease is transmitted by inhalation or contact with infected droplets or fomites, and the incubation period may range from 2 to 14 days[8]. Based on the data from China, the World Health Organisation (WHO) says, on average, a person recovers from Covid-19 in 14 days [3]. It is spreading throughout the globe at a rapid pace and has already caused the destruction of an unprecedented scale, economically, physically, and socially. The reproducibility of the virus, the proportion of asymptomatic carriers, the absence of antibodies of the virus in human bodies, and most importantly, the lack of experience of the people in general in handling such a scenario has contributed to this catastrophe. It has affected more than 3 million people worldwide, and in India, there are 42000 reported cases with 11000 recovered and 1400 dead as of 3rd May, 2020.

With no cure in the immediate future and no immediate possibility of vaccine development (commercial use of a vaccine could take twelve to eighteen months), the Government of India had to rely on suppressive measures such as national lockdown to contain the virus. The purpose of the lockdown is to slow down the spread of the coronavirus so that it doesn’t break the already fragile Indian Healthcare System.

The nationwide Lockdown was announced on 24th March, 2020, and it has been extended until 17th May 2020. On one hand, this lockdown cannot go on indefinitely because of its effect on the daily livelihood of people and economy of the country, and on the other hand, lifting the lockdown, with a significant probability, will result in a huge spike in the rate of infection. At this juncture, the question that seems to be most important to all the policymakers is, when will be the right time to lift the lockdown. In this paper, we modeled the spread of the coronavirus to answer this question. The predictions can be used to form Government policies to contain the virus and to be better prepared for what’s about to come mentally, physically and economically.

**1.1. Epidemiological Model: SIR**

The Susceptible-Infected-Recovered/Removed (SIR) model [5] is a very basic model in Epidemiology to predict the spread of an infectious disease. It considers three different types of compartments for the population, namely susceptible people, infected people, and recovered people. The susceptible compartment consists of people who are vulnerable to the disease, and in the case of Covid-19, it is the entire population except those who have gained immunity after recovering. The differential equation the govern the basic SIR model are:

(1) | |

(2) | |

(3) |

where

*S *= Proportion of Susceptible population

*I *= Proportion of Population who are infected

*R *= Proportion of Population who are recovered, or dead, and thus, immune from future infection *β *= Transmission rate

*γ *= Recovery rate

The equations above describe that

- The fraction of susceptible people decreases as new infections arise and people from Susceptible compartment moves to the Infected compartment.
- The fraction of infected individuals in a population increases by the same rate of decrease of the susceptible population, and a portion of the infected population is either recovered or dead, and hence removed from the Infected compartment and moves to the Removed compartment.

The drawback of the SIR model is that it considers a constant transmission rate *β *throughout the course of the epidemic and does not consider any adopted individual or government measures.

**1.2. Reproduction Number**

Basic Reproduction Number *R*_{0 }is defined as the average number of secondary infections produced by an infected individual when no control measures are taken, and everyone is susceptible. An epidemic results when *R*_{0 }is greater than 1, as there is an exponential rise in the number of cases over time. In the SIR model, it is calculated by dividing the transmission rate(*β*) by the recovery rate(*γ*).

Effective Reproduction Number is defined as the average number of secondary infections produced by an infected individual when transmission occurs in a population that is not entirely susceptible due to implemented control measures. All the control measures aim to reduce the transmission rate so that *R _{t}*, the real-time value of the effective reproductive number, reduces to a value less than 1. This number is dynamic in nature and helps us understand the effectiveness of the adopted control measures. It also helps us to determine whether one should tighten or loosen the restrictions. It is easy to see that

*R*at the start of the epidemic when no control measures are taken and everyone is susceptible is nothing but

_{t }*R*

_{0}.

**1.3. eSIR Model**

The extended SIR model by Song et al. [9] introduced a time-dependent Transmission rate modifier, *π*(*t*) ∈ [0*,*1] to the SIR model we discussed. It considers the time-varying effect of control measures being taken on the transmission rate of the disease. Although the technical discussion of the eSIR model is beyond the scope of this paper, it is important to note that if *π*(*t*) = 1 i.e. no control measures are being taken, then the eSIR model boils down to the standard SIR model.

In their paper Song et al. [9] either takes *π*(*t*) as a continuous pre-defined exponential decay function that assumes steadily increased quarantine and preventive measures or *π*(*t*) as a step function with values that need to be determined empirically. As we don’t know how the transmission rate behaves in response to the adopted control measures in India, instead of using a predetermined *π*(*t*) and assuming the trajectory it will follow, we estimated it directly from the data using the method described in section 2.2.

In section (2), we describe the methodology used to predict the disease progression for the top fifteen most affected Indian states under different possible lockdown relaxation dates (17* ^{th }*May, 31

*may and 14*

^{st }*June) and different levels of social distancing guidelines (Strict, Min, None) that might be adopted post lockdown. In section (3), we present our analysis and predicted plots for the chosen states. In section (4), we conclude with exit strategy recommendations for the chosen states.*

^{th }**2. Methodology**

**2.1. Estimation of R _{t}**

Real-time Effective Reproduction Number gives us information about the evolution of the epidemic, as discussed in section (1). This dynamic number essentially captures the progression of the outbreak in a realistic scenario taking into account everything that affects the spread, including government and individual control measures. It can help us in deciding whether we need to increase the severity of the control measures (If *R _{t }*≥ 1) or if we can afford to relax some restrictions (

*R*1). There are numerous methods proposed by researchers to estimate this value. Taking into account the type of data [1] we have access to for India, we decided to use the method described in a recent paper by Thompson et al. [10] as it only requires the daily number of observed reported cases and the distribution of Serial Interval [7] to estimate

_{t }<*R*. It accounts for uncertainty in the serial interval as precise information about the serial interval might not be available early in an outbreak. One major advantage of this method is that it is that the

_{t}*R*estimates are not affected by asymptomatic cases being unreported as long as the proportion of these unreported cases is constant. This property comes in handy owing to the large percentage of asymptomatic patients in the case of Covid-19. The method in Thompson et al. [10] is implemented in the R package (EpiEstim 2.2). We used the implementation to estimate

_{t }*R*values for the individual chosen states and of India as a country. The resulting plots are shown in Figure 1.

_{t }**2.2. Estimation of Transmission Rate Modifier π(t) from the data**

The transmission rate modifier *π*(*t*) as defined in the eSIR model[6] has the following properties:

*π*(*t*) is a time-varying parameter quantifying the instantaneous effect of control measures adopted by the Government and individuals on the rate of transmission of the infectious disease.*π*(*t*) = 1 when no control measures are taken.

We have mentioned in the introduction and section 2.1 that *R _{t }*captures the effect of all the control measures such as lockdown and social distancing on the rate of transmission of an outbreak and the value of

*R*at the start of the epidemic when no control measures are taken is

_{t }*R*

_{0}. Now, in order to estimate

*π*(

*t*) directly from the data, we calculate

*R*as mentioned in section 2.1, and we derive the value of

_{t }*π*(

*t*) from the estimated

*R*as

_{t}*π*(

*t*)=

*R*.

_{t}/R_{0}The

*π*(

*t*) thus obtained satisfies the properties mentioned in the eSIR model [9] and gives us a transmission rate modifier that is estimated directly from the data. The eSIR model[6] assumes the trajectory that the

*π*(

*t*) will follow under continued restrictive control measures (such as lockdown) by assigning it as an exponential decay function or a step function. In this paper, we have used Seasonal ARIMA, a statistical technique for time-series modeling, to understand the trajectory of

*π*(

*t*) during the lockdown period and used it to model its expected behaviour if lockdown is extended. This was instrumental in getting more robust predictions.

*Figure 1: Real-time Effective Reproduction Number*

**2.3. Exit Strategies and eSIR Model’s Parameter Selection** We define the exit strategies for each state in this section. For each state, we have considered three different lockdown relaxation dates. It is assumed during the duration of the lockdown no relaxations are made in the guidelines.

- 17th May (As specified by the Government)
- 31st May
- 14th June

In the post-lockdown period, we have considered the following three scenarios:

- No Social Distancing: No Individual or Govt. Control Measures being taken and, life continues as it did before the outbreak.
*π*(*t*) = 1 for no control measures. - Minimal Social Distancing: Very minimal social distancing guidelines are followed similar to the time just before the nationwide lockdown was imposed on 24th March 2020.

Using*R*of India calculated in section 2.1,_{t }*π*(*t*) =*R*_{(t=}_{24th march for India}_{)}*/R*_{0 }= 0*.*58

- Strict Social Distancing: India adopts the strategy similar to Wuhan, China, for lockdown relaxation. The lockdown was lifted only when the effective reproductive number dropped very low [4] (less than 0.3 after 8th March), implying the rate of transmission reduced drastically. It was followed by strict Social distancing guidelines. Wuhan has seen no new case for the past two weeks as of 3rd May.

Considering India adopts a similar response, we assume that the lockdown will be relaxed only if*R*has reduced to a value comparable to or less than 0.3 . Post-lockdown, strict social distancing guidelines will be followed, keeping_{t }*R*in check. (less than 0.3)._{t }*π*(*t*) = 0*.*3*/R*_{0 }≈ 0*.*1.

The combination of the these gives us 9 possible exit strategies that we simulated for each state. The implementation of the eSIR model is available in R [6]. We use this implementation of eSIR to predict the disease progression for each state with all nine possible exit strategies. The eSIR model in [6] is solved using a stochastic process, it takes into account uncertainty and generates a distribution of possible outcomes, rather than generating a single deterministic outcome. Markov Chain Monte Carlo algorithm is used to estimate the model parameters of the eSIR model.

**3. Results**

Here we present the results of the predictions made using the eSIR model with the estimated transmission rate modifier for each exit strategy. Each plot is the forecast of trajectory of the infected compartment over time, where the X-axis represents date (time), and the Y-axis represents the fraction of the population that will be infected at the time (cumulative). The observed data points are shown as black dots on the plot, and a blue vertical line marks the last observable date. The green vertical line denotes the first turning point, when the number of daily infected cases start decreasing, and the purple vertical line denotes the second turning point, when the cumulative number of active Covid-19 cases in the population is maximum. The salmon-colored area indicates the 95% confidence interval of the forecast to account for uncertainty.

It is worthy to note, when the *R _{t }> *1, (transmission rate is greater than recovery rate) the number of infected population increases until the peak. As

*R*approaches 1 from a greater value, the height of the peak decreases but it takes longer to reach the peak. The best possible strategy would be to decrease

_{t }*R*1, (transmission rate is less than recovery rate). In this scenario people recover faster than people sick so the number of infected population instead of rising to a peak starts decreasing. This phenomenon can be observed in the following plots and the summary table in section 4.

_{t }<(a) Andhra Pradesh

(b) Bihar

(c) Delhi

(d) Gujarat

(e) Jammu & Kashmir

(f) Karnataka

(g) Kerala

(h) Maharashtra

(i) Madya Pradesh

(j) Punjab

(k) Rajasthan

(l) Telangana

(m) Tamilnadu

(n) Uttar Pradesh

(o) West Bengal

Figure 2: Prediction of Infection under Different Scenario

**4. Conclusion**

Simulating the different scenarios after lockdown, we have found the optimal dates when the lockdown should be relaxed in the 15 most affected states in India. We have coupled this observation with the number of hospital beds available in each state. After combining these two aspects, the following tables summarizes the effect of relaxation of lockdown in the 15 most affected states in India.

The safest proposed exit strategies are highlighted in Blue, considering it does not stress the healthcare system as well as there is no risk of a second wave of infections post Lockdown. The ones that are highlighted in green don’t put stress on the healthcare system but these reach their peak after lockdown meaning a very high risk of second wave of infections post lockdown.

State | No. of beds | No.of beds/ population |
Threshold fraction of infected cases at peak ( at 8% hospitalizationrate) |
Threshold percent of infected cases at peak |

MH | 231739 | 2E-3 | 2.5E-2 | 2.5% |

GJ | 64862 | 1E-4 | 1E-3 | 0.1% |

DL | 39455 | 2.3E-3 | 2.8E-2 | 2.8% |

RJ | 93176 | 1.3E-3 | 1.6E-2 | 1.6% |

TN | 155375 | 2.1E-3 | 2.6E-2 | 2.6% |

MP | 64939 | 9E-4 | 1.1E-2 | 1.1% |

UP | 281402 | 1.4E-3 | 1.7E-2 | 1.7% |

AP | 83230 | 1.6E-3 | 2E-2 | 2.0% |

PB | 60997 | 2.1E-3 | 2.6E-2 | 2.6% |

TG | 99919 | 2.8E-3 | 3.5E-2 | 3.5% |

WB | 113535 | 1.2E-3 | 1.5E-2 | 1.5% |

JK | 7995 | 6E-4 | 7E-3 | 0.7% |

KA | 262109 | 4.2E-3 | 5.2E-2 | 5.2% |

BR | 30857 | 3E-4 | 3E-3 | 0.3% |

KL | 99227 | 2.9E-3 | 3.6E-2 | 3.6% |

**Threshold fraction of infected population at the peak [2]**

MAHARASHTRA | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

Lockdown May | till | 17 | 1. The peak will be reached around June 26 2. 18% of the population will be infected at the peak. |
1. The peak will be reached around July 26 2. 8% of the population will be infected at peak. |
* |

LockdownMay | till | 31 | 1. The peak will be reached around July 10. 2. 15% of the population will be infected at peak. |
1. The peak will be reached around Aug 9 2. 5% of the population will be infected at peak. |
1. The peak will be reached around May 19 2. 0.015% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around July 24 2. 10% of the population will be infected at peak. |
1. The peak will be reached after July 2. <5% of the population will be infected at peak. |
1. The peak will be reached around May 18 2. 0.01% of the population will be infected at peak. |

GUJARAT | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

Lockdown May | till | 17 | 1. The peak will be reached around June 22 2. 17% of the population will be infected at peak. |
1. The peak will be reached around July 22 2. 7% of the population will be infected at peak. |
* |

Lockdown May | till | 31 | 1. The peak will be reached around July 7 2. 15% of the population will be infected at peak. |
1. The peak will be reached around Aug 10 2. 5% of the population will be infected at peak. |
1. The peak will be reached around May 17 2. 0.01% of the population will be infected at peak. |

Lockdown June | till | 14 | 1. The peak will be reached around Jul 23 2. 10% of the population will be infected at peak. |
1. The peak will be reached after July 2. <5% of the population will be infected at peak. |
1. The peak will be reached around May 16 2. 0.01% of the population will be infected at peak. |

DELHI | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around July 6 2. 20% of the population will be infected at peak. |
1. The peak will be reached after July 2. 10% of the population will be infected at peak. |
* |

LockdownMay | till | 31 | 1. The peak will be reached around July 23 2. 18% of the population will be infected at peak. |
1. The peak will be reached after July 2. 8% of the population will be infected at peak. |
1. The peak will be reached around May 11 2. 0.02% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around Aug 8 2. 15% of the population will be infected at peak. |
1. The peak will be reached after August 2. <5% of the population will be infected at peak. |
1. The peak will be reached around May 11. 2. 0.02% of the population will be infected at peak. |

RAJASTHAN | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 18 2. 12% of the population will be infected at peak. |
1. The peak will be reached around July 13 2. 5% of the population will be infected at peak. |
* |

LockdownMay | till | 31 | 1. The peak will be reached around July 1 2. 7% of the population will be infected at peak. |
1. The peak will be reached around July 28 2. 3% of the population will be infected at peak. |
1. The peak will be reached around May 16 2. <0.01% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around July 20 2. <2% of the population will be infected at peak. |
1. The peak will be reached after July 2. <1% of the population will be infected at peak. |
1. The peak will be reached around May 16 2. <0.01% of the population will be infected at peak. |

TAMIL NADU | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 20 2. 12% of the population will be infected at peak. |
1. The peak will be reached around July 25 2. 4% of the population will be infected at peak. |
* |

LockdownMay | till | 31 | 1. The peak will be reached around July 7 2. 5% of the population will be infected at peak. |
1. The peak will be reached around August 7. 2. 2.5% of the population will be infected at peak. |
1. The peak will be reached around May 15 2. 0.005% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around July 22 2. 2.5% of the population will be infected at peak. |
1. The peak will be reached after July 2. 0.5% of the population will be infected at peak. |
1. The peak will be reached around May 15. 2. 0.005% of the population will be infected at peak. |

MADHYAPRADESH | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 23 2. 8% of the population will be infected at peak. |
1. The peak will be reached around Aug 3 2. 2.5% of the population will be infected at peak. |
1. The peak will be reached around May 3 2. 0.003% of the population will be infected at peak. |

LockdownMay | till | 31 | 1. The peak will be reached around July 13 2. <3% of the population will be infected at peak. |
1. The peak will be reached after July 2. <1% of the population will be infected at peak. |
1. The peak will be reached around May 3 2. 0.003% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around July 31 2. 0.3% of the population will be infected at peak. |
1. The peak will be reached around Aug 30 2. 0.15% of the population will be infected at peak. |
1. The peak has been reached around May 3 2. 0.003% of the population will be infected at peak. |

UTTARPRADESH | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 15 2. 10% of the population will be infected at peak. |
1. The peak will be reached around July 8 2. 5% of the population will be infected at peak. |
* |

LockdownMay | till | 31 | 1. The peak will be reached around June 29 2. 3% of the population will be infected at peak. |
1. The peak will be reached around July 25 2. 1% of the population will be infected at peak. |
1. The peak will be reached around May 10 2. 0.002% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around July 12 2. 1% of the population will be infected at peak. |
1. The peak will be reached around July 28 2. 0.5% of the population will be infected at peak. |
1. The peak will be reached around May 9 2. 0.002% of the population will be infected at peak. |

ANDHRAPRADESH | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around July 21 2. 5% of the population will be infected at peak. |
1. The peak will be reached after August 2. <2% of the population will be infected at peak. |
* |

LockdownMay | till | 31 | 1. The peak will be reached after Aug 2. 3% of the population will be infected at peak. |
1. The peak will be reached after Aug 2. <1% of the population will be infected at peak. |
1. The peak has been reached around May 3 2. 0.003% of the population will be infected at peak |

Lockdown June | till | 14 | 1. The peak will be reached after Aug 2.<1% of the population will be infected at peak. |
1. The peak will be reached after Aug 2. <0.5% of the population will be infected at peak. |
1. The peak has been reached around May 3 2. 0.003% of the population will be infected at peak. |

PUNJAB | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 11 2. 15% of the population will be infected at peak. |
1. The peak will be reached around July 1 2. 6% of the population will be infected at peak. |
* |

LockdownMay | till | 31 | 1. The peak will be reached around June 26 2. 15% of the population will be infected at peak. |
1. The peak will be reached around July 17 2. 5% of the population will be infected at peak. |
* |

LockdownJune | till | 14 | 1. The peak will be reached around July 11 2. 13% of the population will be infected at peak. |
1. The peak will be reached around Aug 2 2. 5% of the population will be infected at peak. |
1. The peak will be reached around May 28 2. 0.25% of the population will be infected at peak. |

TELANGANA | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 18 2. 6% of the population will be infected at peak. |
1. The peak will be reached around July 20 2. 2.5% of the population will be infected at peak. |
1. The peak has been reached around April 24 2. <0.003% of the population infected at peak |

LockdownMay | till | 31 | 1. The peak will be reached around July 5 2. <3% of the population will be infected at peak. |
1. The peak will be reached around Aug 5 2. <1% of the population will be infected at peak. |
1. The peak has been reached around April 24 2. <0.003% of the population infected at peak |

LockdownJune | till | 14 | 1. The peak will be reached around Aug 6 2. 0.3% of the population will be infected at peak. |
1. The peak will be reached around July 29 2. 0.15% of the population will be infected at peak. |
1. The peak has been reached around April 24 2. <0.003% of the population infected at peak. |

WEST BENGAL | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 18 2. 5% of the population will be infected at peak. |
1. The peak will be reached around July 23 2. 2% of the population will be infected at peak. |
* |

LockdownMay | till | 31 | 1. The peak will be reached around July 7 2. 2% of the population will be infected at peak. |
1. The peak will be reached after July. 2. <1.5% of the population will be infected at peak. |
1. The peak will be reached around May 13 2. 0.0025% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around July 29 2. 1% of the population will be infected at peak. |
1. The peak will be reached after Aug 2. <0.5% of the population will be infected at peak. |
1. The peak will be reached around May 13 2. 0.0025% of the population will be infected at peak. |

JAMMU AND KASHMIR | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 29 2. 10% of the population will be infected at peak. |
1. The peak will be reached around August 4 2. 2.5% of the population will be infected at peak. |
1. The peak has been reached around April 30 2. 0.003% of the population will be infected at peak. |

LockdownMay | till | 31 | 1. The peak will be reached around July 15 2. 3% of the population will be infected at peak. |
1. The peak will be reached after July 2. <2% of the population will be infected at peak. |
1. The peak has been reached around April 30 2. 0.003% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around Aug 6 2. 1% of the population will be infected at peak. |
1. The peak will be reached after Aug 2. <1% of the population will be infected at peak. |
1. The peak has been reached around April 30 2. 0.003% of the population will be infected at peak. |

KARNATAKA | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 13 2. 5% of the population will be infected at peak. |
1. The peak will be reached around July 4 2. 1% of the population will be infected at peak. |
1. The peak has been reached around April 25 2. 0.001% of the population will be infected at peak. |

LockdownMay | till | 31 | 1. The peak will be reached around July 1 2. 1% of the population will be infected at peak. |
1. The peak will be reached around July 14 2. 0.3% of the population will be infected at peak. |
1. The peak has been reached around April 25 2. 0.001% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around July 28 2. 0.07% of the population will be infected at peak. |
1. The peak will be reached after July 2. <0.07% of the population will be infected at peak. |
1. The peak has been reached around April 25 2. 0.001% of the population will be infected at peak. |

BIHAR | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around July 11 2. 3% of the population will be infected at peak. |
1. The peak will be reached after July. 2. <1.5% of the population will be infected at peak. |
1. The peak will be reached around May 4. 2. 0.002% of the population will be infected at peak. |

LockdownMay | till | 31 | 1. The peak will be reached around Aug 10 2. 1% of the population will be infected at peak. |
1. The peak will be reached after Aug 2. 0.25% of the population will be infected at peak. |
1. The peak has been reached around May 4. 2. 0.002% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached after Aug 2. 0.3% of the population will be infected at peak. |
1. The peak will be reached after Aug 2. 0.1% of the population will be infected at peak. |
1. The peak has been reached around May 4. 2. 0.002% of the population will be infected at peak. |

KERALA | |||||

Lockdown followed by: | No Social Distancing | Minimal Social Distancing | Strict Social Distancing | ||

LockdownMay | till | 17 | 1. The peak will be reached around June 26 2. 2% of the population will be infected at peak. |
1. The peak will be reached around July 6 2. 0.2% of the population will be infected at peak. |
1. The peak has been reached around April 8. 2. 0.001% of the population will be infected at peak. |

LockdownMay | till | 31 | 1. The peak will be reached around July 14 2. 0.08% of the population will be infected at peak. |
1. The peak will be reached around July 27 2. 0.025% of the population will be infected at peak. |
1. The peak has been reached around April 8. 2. 0.001% of the population will be infected at peak. |

LockdownJune | till | 14 | 1. The peak will be reached around July 27 2. 0.06% of the population will be infected at peak. |
1. The peak has been reached around April 8. 2. 0.001% of the population will be infected at peak. |
1. The peak has been reached around April 8. 2. 0.001% of the population will be infected at peak. |

*: According to the definition of this exit strategy in section 2.3, Lockdown only lifted if *R _{t }*drops to a value comparable to 0.3. In this case the

*R*is still high implying that the rate of transmission is high. Hence this scenario is not simulated.

_{t }To summarise the findings from the tables above, we conclude

- Most of the states will reach its peak before May 18 under Lockdown with the exception of Punjab. But the fate of the state is decided by how the people act after the lockdown is lifted. If strict social distancing guidelines are not followed then the infection curve that already peaked during lockdown will start rising again and give rise to a second wave of infections with peak that is higher in magnitude and will take more time to reach.

Take the example of Kerala, that even though the peak has already been attained under lockdown at the beginning of April and the number of active cases is on the decline, the simulation shows that it can only be safe to lift the lockdown after 17th May or 31st May if we follow very Strict Social Distancing post lockdown. But if we don’t adhere to such guidelines then there is a high risk of cases rising again giving way to a second wave of infections that will affect more people than the healthcare capacity of the state and will reach its peak in June/July. - For most of the states(except Punjab) it can be expected to lift the lockdown on or before 31st May if we are capable of following strict Social Distancing guidelines afterwards.
- In Punjab’s case it is highly recommended to monitor the situation closely and extend lockdown until 14th June. It is interesting to note that even though Maharashtra has the highest number of infections, it is Punjab that is expected to reach its peak last around May 28, that too only if Lockdown in Punjab is extended.

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