Assessment of lockdown effect in some states and overall India: A predictive mathematical study on COVID-19 outbreak

Abstract

In the absence of neither an effective treatment or vaccine and with an incomplete understanding of the epidemiological cycle, Govt. has implemented a nationwide lockdown to reduce COVID-19 transmission in India. To study the effect of social distancing measure, we considered a new mathematical model on COVID-19 that incorporates lockdown effect. By validating our model to the data on notified cases from five different states and overall India, we estimated several epidemiologically important parameters as well as the basic reproduction number (R ₀). Combining the mechanistic mathematical model with different statistical forecast models, we projected notified cases in the six locations for the period May 17, 2020, till May 31, 2020. A global sensitivity analysis is carried out to determine the correlation of two epidemiologically measurable parameters on the lockdown effect and also on R ₀. Our result suggests that lockdown will be effective in those locations where a higher percentage of symptomatic infection exists in the population. Furthermore, a large scale COVID-19 mass testing is required to reduce community infection. Ensemble model forecast suggested a high rise in the COVID-19 notified cases in most of the locations in the coming days. Furthermore, the trend of the effective reproduction number (R_t ) during the projection period indicates if the lockdown measures are completely removed after May 17, 2020, a high spike in notified cases may be seen in those locations. Finally, combining our results, we provided an effective lockdown policy to reduce future COVID-19 transmission in India.

Keywords: COVID-19; Lockdown effect; Mathematical model; Outbreak containment policy.

Fig. 1

Flow diagram of the mathematical model with lockdown. Epidemiological information of different parameters shown in the above figure are provided in Table 1.

Fig. 2

Three models (mechanistic mathematical model, statistical forecast model and ensemble model) fitting to daily notified COVID-19 cases from five different states and overall India for the period March 14, 2020 till May 3, 2020. Respective subscript are MH: Maharashtra, DL: Delhi, TN: Tamil Nadu, GJ: Gujarat, PJ: Punjab, and IND: India. Here LD denotes lockdown period and No LD indicate the period before lockdown implementation. Statistical forecast model for different locations are ARIMA (DL and GJ), TBATS (PJ) and HYBRID (MH, TN and IND), respectively. Lockdown effect is only considered for the mechanistic mathematical model and consequently in the ensemble model. Shaded area indicate the 95% confidence region.

Fig. 3

Global sensitivity analysis of two epidemiologically measurable parameters namely κ: fraction of new infected that become symptomatic and τ: average notification & hospitalization rate of symptomatic COVID-19 infection, on R₀. The subscripts MH, DL, TN, GJ, PJ and IND, respectively are same as Fig 2.

Fig. 4

Ensemble model forecast for the daily notified COVID-19 cases in India during May 17, 2020 till May 31, 2020, under five different social distancing measure. Various legends are Current Rate: daily notified case projection using the estimated value of the lockdown rate (see Table 2), 15% Reduction: daily notified case projection using 15% reduction in the estimated value of the lockdown rate (see Table 2), 20% Reduction: daily notified case projection using 20% reduction in the estimated value of the lockdown rate (see Table 2), 30% Reduction: daily notified case projection using 30% reduction in the estimated value of the lockdown rate (see Table 2), and No lockdown: daily notified case projection based on no lockdown scenario, respectively.

Fig. 5

Global sensitivity analysis of two epidemiologically measurable parameters namely κ: fraction of new infected that become symptomatic and τ: average notification & hospitalization rate of symptomatic COVID-19 infection, on the lockdown effect. The effect of lockdown is measured as the difference between the total number of cases projected by our ensemble model with and without lockdown scenario during May 17, 2020 till May 31, 2020. The subscripts MH, DL, TN, GJ, PJ and IND, respectively are same as Fig 2.

Fig. 6

Effective reproduction number (R_t) for the period May 17, 2020 till May 31, 2020, in MH, DL, TN, GJ, PJ and IND, respectively. The subscripts MH, DL, TN, GJ, PJ and IND, respectively are same as Fig 2.