key: cord-277128-g90hp8j7 authors: Rajendran, Sukumar; Jayagopal, Prabhu title: Accessing Covid19 Epidemic Outbreak in Tamilnadu and the Impact of Lockdown through Epidemiological Models and Dynamic systems date: 2020-09-17 journal: Measurement (Lond) DOI: 10.1016/j.measurement.2020.108432 sha: doc_id: 277128 cord_uid: g90hp8j7 Despite having a small footprint origin, COVID-19 has expanded its clutches to being a global pandemic with severe consequences threatening the survival of the human species. Despite international communities closing their corridors to reduce the exponential spread of the coronavirus. The need to study the patterns of transmission and spread gains utmost importance at the grass-root level of the social structure. To determine the impact of lockdown and social distancing in Tamilnadu through epidemiological models in forecasting the “effective reproductive number” (R(0)) determining the significance in transmission rate in Tamilnadu after first Covid19 case confirmation on March 07, 2020. Utilizing web scraping techniques to extract data from different online sources to determine the probable transmission rate in Tamilnadu from the rest of the Indian states. Comparing the different epidemiological models (SIR, SIER) in forecasting and assessing the current and future spread of COVID-19. R(0) value has a high spike in densely populated districts with the probable flattening of the curve due to lockdown and the rapid rise after the relaxation of lockdown. As of June 03, 2020, there were 25,872 confirmed cases and 208 deaths in Tamilnadu after two and a half months of lockdown with minimal exceptions. As on June 03, 2020, the information published online by the Tamilnadu state government the fatality is at 1.8% (208/11345=1.8%) spread with those aged (0-12) at 1437 and 13-60 at 21899 and 60+ at 2536 the risk of symptomatic infection increases with age and comorbid conditions. The thrust of this global Pandemic is disrupting the natural flow of human existence via COVID-19 of the "common cold" coronavirus family, its existing versions of a severe acute respiratory syndrome (SARS) (2001) (2002) (2003) , and middle east respiratory syndrome (MERS) (2012) (2013) (2014) (2015) . SARS-CoV and covid19 spread from infected civets and bats, while MERS-CoV originated from dromedary camels resulting in an epidemic as corroborated by scientific research. This paper intends to provide a detailed view of the different mathematical models in predicting the rife of covid19. Modeling a detailed view in determining the spread of covid19 taking into account the influences of provincial factors, thereby providing a fundamental understanding through quantitative and qualitative inferences during these uncertain times. The model utilizes population dynamics and conditional dependencies such as new cases, deaths, social distancing, and herd immunity over a stipulated timeperiod to simulate probable outcomes. The social stigma determines the rate of spread and is specific to the region and religious practices and different structure congregation of the masses. A thorough study of different epidemiological models is presented in the subsequent section and the comparative analysis of the various factors and socio-economic needs that influence the model's capabilities in determining the spread of the epidemic. The epidemiological model provides a system to define and determine interventions based on statistics of collected data and predicting the probability of determining the development prevention and control of diseases. Epidemiology models are classified into respective categories based on the chance variations (stochastic & deterministic), time (continuous & discrete intervals), space (spatial & non-spatial), and population (homogenous & heterogenous) to predict the dispersion of diseases (Hethcote, 2000) . The factors governing the spread are infectious agents, modes of transmission, susceptibility, and immunity (Chowell et al., 2006 The case fatality rate(CFR) is highly variable and increases with severe respiratory symptoms in adults with comorbid conditions . There present scenario specified in this paper is currently no specific vaccine available for covid19, despite quarantines and lockdowns imposed. the authors also specify a need to accelerate protocols to rapid point of care diagnostic testing and effective personal care in preventing the transmission and spread of the disease. The authors provide a time dependent model more adaptive than the existing models but with a way of further improving the results and predictions by taking into account the disease propagation probabilities and transmission rates (Del Rio & Malani, 2020). The portals and dashboard created by WHO (Organisation, n.d.) and Tamilnadu  Utilize a language library(python) designed for covid19. The Reed-Frost Theory (Abbey, 1952) represents Soper's equation as follows (1) The proposed equation 1 helps in determining the cases in successive time periods. Where → number of cases, t time and probability of an individual with no contact with , → → 1 -→ probability of an individual having contact with . The Reed-Frost Theory (Abbey, 1952) states that (2) and For a population of A and B, the theory states in equation 4 that individual is not infected from cases in population B . (4) But is infected from any one of the cases in either of population A or B 1 -. (5) The cases infected from the population A in time t+1 is The cases infected from the population B in time t+1 is Both equations 6 & 7 determined the introduction of cases into the population, which forms the initial spread for epidemics. The compartmental structure of different epidemiological models SI, SIS, SIR, SIRS, SEI, SEIS, SEIR, SEIRS, MSEIR, MSEIRS, are represented in figure 1, The dynamics of covid19 are mapped into a compartmental model that generates the mean-field approximations to ensemble or population dynamics four latent factors determine the distributions i. Location The transmission probability iv. Diagnostic and testing the master equation for the dynamic part of the dynamic casual model is Case fatality rate (CFR) = Number of people died The reproductive number (R 0 ) called "R naught" defines the average number of secondary infections caused by an infected individual introduced into an uninfected population. The range of >1 0 signifies an epidemic while <1 defines the disease as eliminated. There has been a high spread from the interstate and intercontinental travelers to Tamilnadu state. Air & rail travel has eased the transmission and spread of the covid19 diseases in rural and urban districts of Tamilnadu. The statistics are as follows To measure the clustered spread of covid19 is to determine the geolocation of the infected individual as the individual is entering into the community with zero infected individuals (Sugiura, 1978) . In order to measure the intensity of the spread, each individual is measured as the centroid of the cluster (Li et al., 2020) . The dependent features are the age, embarking source, and destination vectors (Chowell et al., 2006) . The specific clusters identified in Tamilnadu are that of the Delhi cluster, Koyambedu cluster (Majumder & Mandl, 2020) . The data defined with that of the cluster is as shown in the table The age-structured epidemiological models are differential equations specific to the changing size and age structure of a population over time. These models work on continuous age and age groups as partial and ordinary differential equations. The continuous age model is determined with a partial differential equation for the population growth. A demographic model with Continuous Age This population model called the Lotka -Mckendrick Model (Barbu et al., 2001) . The classic Kermack-Mckendrik model Where These class-age-structured model equations are The initial population age distribution epidemiological model assumes that there is a steady age distribution in the total population size. A demographic model with Age groups The government of India and the state of Tamilnadu implemented lockdown for four periods as lockdown 1.0 to 4.0 from March till May and further extending with leniency. This lockdown has reduced the rapid spread of covid19 through social distancing, reducing fatalities. The three main transmission modes through physical contact, respiratory droplets through sneezing or < 5 coughing, indirect contact with surfaces handled by an infected person. In this stage, the probability transmission is from traveling individuals from different geographical locations, the sources are highly identifiable, and isolation is high. The isolated individuals infect a small cluster of the surrounding, thereby creating sporadic pockets of infection. Individual identified within the local cluster . In this stage, the source is not identifiable, and vast masses of people are infected. The infection spreads through random patterns where random members start to get infected. denotes the travel of the individual from state, district, international locations. → In this stage, the spread becomes an epidemic with a large number of infected people and an increase in the number of deaths. After a while, the community starts to develop immunity to this specific strain of the virus, thereby reducing transmission and death eventually. There is also a possibility of the virus mutating generating a second wave. The mapping of transmission of covid19 is done through contact tracing, thereby isolating individuals infected by the epidemic at different epicentres of the society denoted by . Lockdown reduced the spread of covid19 in Tamilnadu as represented in dotted lines in the figure below. 3-18-2020 3-20-2020 3-22-2020 3-24-2020 3-26-2020 3-28-2020 3-30-2020 4-1-2020 4-3-2020 4-5-2020 4-7-2020 4-9-2020 4-11-2020 4-13-2020 4-15-2020 4-17-2020 4-19-2020 4-21-2020 4-23-2020 4-25-2020 4-27-2020 4-29-2020 5-1-2020 5-3-2020 5-5-2020 5-7-2020 5-9-2020 5-11-2020 5-13-2020 5-15-2020 5-17-2020 5-19-2020 5-21-2020 5-23-2020 5-25-2020 5-27-2020 5-29-2020 5-31-2020 6-2-2020 Lock Down Period in The attack rate contributes to the different cycles and the modes of the transmission of covid19. The implication depends on the population cluster size and the number of infected cases. Secondary attack rate The SAR is the infectability rate of the individuals already infected by covid19 and recovered. The SAR contributes to the identification of the whether recovered patients are immunized for lifetime or for a few months. The infected person enters the population and transmits to each person with probability p. k the number of people re-infected while being contagious for transmission of secondary infections (Kharroubi, 2020 ). transmitting contact (Efimov & Ushirobira, 2020) . The differential = -- Let be birth and death rate, The probabilistic model process through different nodes as infected and recovered (Yan et al., 2020) . ≈ ( ) ∑ ∈ ( ) ( ) = ( ) SI model SIS model SIR model SEIR model The figure below shows Indian state/UT wise details of Active cases of covid19 Pandemic in India till June 04. In this proposed study of covid19 infection in Tamilnadu, the dataset consists of cases district wise till 31 may 2020 is used. The status of individual district details is extracted from the Health & family welfare department government of Tamilnadu. The district-wise details of the covid19 status displayed in the sample table 2 27 Thirupathur 32 28 4 0 28 Thiruvallur 948 603 334 11 29 Thiruvannamalai 419 144 273 2 30 Thiruvarur 47 33 14 0 31 Thoothukudi 226 135 89 2 32 Tirunelveli 352 211 140 1 33 Tiruppur 114 114 0 0 34 Trichy 88 70 18 0 35 Vellore 43 The different statistical measure models have evolved to predict the transmission of infectious viruses/ bacteria. The different measures taken into account depends on the geographical structure, climatic condition, and region-specific human practices. The infectious pathogens follow specific traits while infecting and spreading from host to host, creating a life cycle. The transmission rate and intensity may vary between interspecies transmission and human transmission, depending on whether the transmission is direct or intermediary. The infection rate is very low at the initial transmission between interspecies, while there is an exponential increase in human transmission. The study of Covid19 spread in Tamilnadu The transmission of infection from infected to the susceptible persons is at 5,40,405. The recovery rate and the comorbidity rate of the covid19 varies predominantly as the geographical and climatic changes influence the spread. The attack rate and the susceptibility rate rapidly increase due to the adaption of the virus strain pertaining to the individual's genetic morphology. The susceptible individuals are isolated with the impact of lockdown reducing the susceptibility rate of covid19. The time the infectious disease doubles in number with as the initial number of infected cases 0 doubling period of the cases and the initial number of infected cases at time t. The initial time and the doubling time taken to reproduce is reduced to seven days as the spread of the infection amplifies with the different strains and clusters of infection. The peak period of the infection is gradually increased as the imposition of the lockdown reduces the transmission cycle of covid19. This model represents the SIR epidemic Model for Indian states with different geographical regions. The data is collected for a period of two and a half months and pre-processed to remove the missing and noisy data [13]- [19] . The transformation from raw data to geospatial data is possible through QGIS, and mapping the shapefiles created through ArcGIS [5]- [12] . A sample of the mapped data is, as shown in figure 14 . The Daily Testing statistics of the covid19 per lakh population in Tamilnadu is at 865 as on 15-06-2020 with the number of persons tested is at 6,42,201, and the number of samples tested is at 7,10,599. The daily testing statistics of the covid19 per lakh population in Tamilnadu is at 3760 as on 08-08-2020 with the number of persons tested is at 29,75,657. Based on the data provided by the government of Tamilnadu, the SIR model, compared with the other compartmental model's project, the outbreak will peak at the end of June and will start decreasing towards the end of August. Based on this model and the different parameters like the lockdown and the social distancing and applying face mask has postponed the infectious rate of transmission through May 2020 to June 2020. The proposed model compares the age/ gender wise social distancing to be for comparison through the dynamic models. The model specifies Doubling time and the attack rate at which the infection spreads. The inclusion of Tamilnadu State district wise rate of attack is necessary to determine the rate of spread of Covid19 at the district, town, and village panchayat levels. The flattening of the curve is ascertained by the end of August in Tamilnadu as the R 0 values are at an inflection point where the curve attains the period of a downtrend as the herd immunity increases as social distancing and personal protection becomes a daily ritual. The estimated values of the data should be interpreted with caution as the data may vary based on the climatic condition, geographical variations and frequential history of susceptibility to infectious diseases. The important findings are to impose lockdowns that supress the transmission of the diseases, and isolate individuals with comorbidity. The covid19 value varies considerably for 0 different models and moreover the reinfection rate of the already infected is unknown and the future impact of subsequent fatalities are unknown. The mathematical numerical analysis conducted in the paper is more adaptive than the traditional models. The model can be extended to study the infective rate and the asymptotic infectious rate by including both the infected and the asymptotic undetected individuals. The model can be extended to other states characterized by similar geographic and climatic conditions and a closer reproductive rate . An examination of the Reed-Frost theory of epidemics On the controllability of the Lotka--McKendrick model of population dynamics A Time-dependent SIR model for COVID-19 with undetectable infected persons Mathematical applications associated with the deliberate release of infectious agents COVID-19-new insights on a rapidly changing epidemic On an interval prediction of COVID-19 development based on a SEIR epidemic model The mathematics of infectious diseases Modeling and predicting the spread of COVID-19 in Lebanon: A Bayesian perspective Predicting the epidemic trend of COVID-19 in China and across the world using the machine learning approach Early transmissibility assessment of a novel coronavirus in Wuhan d.). {Ministry of Health and Family Welfare}, year = 2020 d.). {World Health Organisation Covid19}, year = 2020 Further analysts of the data by akaike's information criterion and the finite corrections: Further analysts of the data by akaike's An interpretable mortality prediction model for COVID-19 patients Writing-Original draft preparation We authors confirm that there is no conflict of interest associated with research work carried out with any means.Further, we confirm, the article not submitted elsewhere to any journal or conference, solemnly set for Measurement Journal, Elsevier Publications for the review process. In addition, no funding resources are available for this research activity.