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On Containment Plan Amid COVID-19 in Red Zone Districts of India: Using Clinical Life Table and Cure Fraction Model

Background and Objective: Ministry of Health and Family Welfare, Government of India took many measures to arrest the spread of COVID-19 disease. This research is intended to shed light on number of confirmed cases with respect to population density of the affected districts, to study the proportion of positives among total sample tested, to construct clinical life table of general population w.r.t. number of daily positive cases and to estimate the long-term survivors among general population. Materials and Methods: Simple scatter plot has been used to see relation between population density and number of cases in different districts of India, cluster analysis technique is used for making cluster of Districts having similar features. Clinical life table is prepared for general population of affected Districts, and mixture & non-mixture cure fraction models used to estimate the proportion of long-term survivors (disease free survival) of general population. Result: Median daily proportion of positives are found to be below 0.05. In 79 identified hot spot Districts average population is very high (36.29 lakhs) with population density of 3404 per square kilometre. Even among those Districts there are huge inter cluster differences w.r.t. number of cases and population density. Clinical life table is constructed for general population of 429 affected Districts, increasing pattern in hazard is found even though study period is small. Long term survivors of disease is simulated and found to be 99.812%. Conclusion : Government ought to make cluster of Districts among red zone Districts, clustering should be based on number of cases and population density. Different containment strategy may be prepared for each cluster of Districts.


Introduction
Whole world is facing the biggest public health crisis of century, the current coronavirus disease came into global discourse on December 31, 2019, the day China notified the World Health Organization about pneumonia of an unknown genesis. Disease first appeared in Wuhan city of Hubei Province of China. The disease spread to more Provinces of China in ensuing days and further to the whole world. The outbreak was declared a Public Health Emergency of International Concern on January 30, 2020. 1,2 From the daily situation report published by WHO on April 20, 20203, total confirmed cases are 2314621 and total deaths due to COVID-19 are 157847. For the South East Asia region (India, Indonesia, Thailand, Bangladesh, Sri Lanka, Myanmar, Maldives, Nepal, Timor-Leste, Bhutan) total cases till 19 April 2020 are 29576 and total deaths are 1225.
In this region, India alone accounts for 58.37% of the total cases and 44.32% of the total deaths. In Indonesia the pandemic has taken community transmission route and all other countries are either on sporadic cases detection phase or on cluster of cases detection phase.
To limit the spread of transmission and death toll Government of India is taking all necessary measures but India being a democratic republic it ought to strike a fine optimal strategy in protecting health, minimizing economic and social unsettling, and respecting human rights.
In India pandemic first set foot in the State of Kerala on January 30, 2020. In very short span of time it is wreaking havoc all over India except for North-Eastern States. Indian Council of Medical Research (ICMR) is spearheading the pandemic management through its various arms spread across the country. It formulates guidelines, coordinates with related government agency/ ministry, promotes research and development of associated treatments and preventions.
The current testing strategy (April 9, 2020) released by ICMR is as follows: All symptomatic individuals who have undertaken international travel in the last 14 days. All symptomatic contacts of laboratory confirmed cases, all symptomatic health care workers. All patients with Severe Acute Respiratory Illness (fever AND cough and/or shortness of breath), Asymptomatic direct and high-risk contacts of a confirmed case should be tested once between day 5 and day 14 of coming in his/ her contact.
The paper is designed as follows: in the next section 2, various data sources and brief explanation of methods to be used are given. In section 3 results and implications are provided followed by section 4, where final conclusion and insights drawn from research are presented.

Material
The data of total number of cases, daily number of tested has been scrapped from crowd sourced website https://www. covid19india.org/, population data from census of India 2011 (http://censusindia.gov.in/) and population density from District of India website (http://districts.nic.in/). To update the population of the Districts to the current time, the annual population growth rate data was used from the published reports of World Bank (https://data.worldbank. org/indicator/SP.POP.GROW?locations=IN). Other sources of COVID-19 data are John Hopkins (https://coronavirus. jhu.edu/), World Health Organization's daily situation report (https://www.who.int/emergencies/diseases/novelcoronavirus-2019/situation-reports). But for this study COVID-19 data only taken from first source.

Method
Cluster Analysis is a data mining technique where clusters are formed from the objects/observations that belongs to same class. Here similar objects are grouped in one cluster and dissimilar objects are grouped in another cluster, clustering will be performed using R software package version 3.5.2. Most of times cluster analysis is used as a pre-processing step for other statistical techniques and algorithms. It is applied in marketing, land use study, insurance, city planning, medical imaging etc. 5,6 Clinical Life Table   As name suggest this life table technique Where, Su(t) is the survival function of the susceptible population which may be assumed to follow some life time distribution. Probability density function f(t) of the overall population is written as: Consequently, the individual's contribution to the likelihood function can be written as: ( 3) Hence, complete likelihood is given by: Parameters can be estimated by maximizing the complete data likelihood in equation (4) using Open BUGS software package using Gibbs sampling approach. [11][12][13][14][15][16][17][18] Non-Mixture Cure Rate Model In order to accommodate the changes (like second and third wave of disease that reduces event free survival that may occur during the study, a non-mixture cure rate models can be used. It is defined as: Where 'C' is the probability of an Individual being long-term survivor and Fu(t) = 1-Su(t) is the distribution function for susceptible individual.
In the model (5), i th (i= 1, 2, . . , n) individual's contribution in the likelihood function can be written as: Hence, complete data likelihood is given by: here product if from i=1 to n parameters of the above two models will be estimated by Gibbs sampling in the Bayesian framework. 19 Result Table 1, presents the country data obtained from crowd sourced data repository that take feed from various updates published by ICMR on almost real time basis. Daily proportion of positives is calculated as daily positives/daily tested, Figure 1 shows the simple bar plot of daily number of tested and daily number of positives. Due to some discrepancy in observation and unavailability of data only up to 19 April 2020 cases are taken.     For 79 hot spot Districts correlation between population density and number of cases 0.2166 (and is significant at 10% confidence level). Figure 3 gives the simple scatter plot between population density and cumulative cases in 79 identified hot spot Districts. By visually inspecting the graph, one may get the rough idea about similarities between Districts with respect to density and cases.
In order to make cluster of Districts, a normalization of variable is performed (to change the values of numeric variable into a common scale). K means clustering algorithm has been employed to accomplish the cluster-making task. Graph (Figure 4)   129.75 (which seems quite low as compared to cluster 1 and cluster 3) but that cluster has very high average population density of 21659.12 per square kilometre, which is alarming, as higher the population density there is higher risk of disease proliferation.   Figure 5, shows the survival function plotting, clearly the slope is in downward direction. Although, decrement is quite small but when one think in terms of general population it will give significant number of infected persons in short lap of time. Figure 6 and 7 gives the hazard and cumulative hazard plotting of general population.   Define event of interest as "onset of COVID-19" with baseline as 1 April 2020 for general population then the survival time for each individual will be "COVID-19 free survival". As mentioned earlier, the observation period of this study is first 19 days of April month. So, keeping in mind the highly contagious nature of disease if we assume that those who are COVID free during this period are longterm survivors. We simulated one million data points to get survival times, on applying mixture and non-mixture cure fraction model using Open BUGS software package we get the following results (Table 5). From table the model that gives least DIC value is exponential mixture cure model with DIC value of 370.2 and cure fraction 0.99812, i.e. after 19 days of pandemic (base shifted to 1 April) around 99.812% of general population will be COVID-19 free.

Conclusion
Without thorough study, temporary measures like contentious blanket lockdown the resulting slowing down of economy is inevitable. Due to this COVID-19 menace, global giant economies are at cusp of following the rocky path ahead.
To mitigate the repercussions of COVID-19 containment, strategist should prepare the plan at micro level amidst pandemic.
Currently Government of India is segregating Districts in red, yellow and green zones. Here we suggest to augment the plan for red zone Districts. There should be different cluster containment plans for various Districts that falls into red zone. Each District ought to have plan based on clinical life table for general population. Life table must be fed with data pertaining to migration of people to/ from the District, birth, death due to natural causes, death due to other diseases, death due to accidents.
If provided data on proper COVID-19 free survival for each District then probabilistic models like cure fraction can be used to find proportion of long-term survivors in foreseeable future that would be helpful in planning.