Analysis of SIR Network Model on COVID 19 with respect to its impact on West Bengal in India

The recent global pandemic of SARS-CoV-2 (COVID-19) disease has prompted many researchers to formulate lock-down and quarantine scenarios while the main concern of the researchers is to model the spread and the possible duration of the COVID-19 infections and also research on how long this is going to last. It seems that most of the researchers have recognized lock-down as one of the major impact factors in their models. As a result of this in the absence of lock-down the models formulated would not contribute much significant results. Hence, in this work we decide to formulate a mathematical model which would be able to predict the spread and also the possible duration of the pandemic, by considering both partial lock-down and the corresponding unlocking situations. Employing SIR-network models and taking the various districts of highly populated areas of West Bengal, India as the nodes or vertices we attempt to model the spread and duration of the pandemic during both partial lock-down and unlock phases but separately. We consider the populations where the locally present people and the people who have undergone migration of some shorts are well mixed together. In the network that we have provided the pointed edges refer to the migrating workers that is those that move away from their regular habitats in want of work. We use this research to study not only the trends that are associated with COVID-19 outbreaks, but also to study the impacts of the Government policies and the improvisation of medical facilities on this outbreak in West Bengal. At the end, we attempt to throw light upon the crisis that the economy of the state may have to go through separately on partial lock-down and unlocking scenarios. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement No funding. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: Approved. All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes There are practical difficulties in resolving the actual number of infections, since most cases of covid-19 are non-communicable or the symptoms are influenzalike, for example. Unfortunately, the data obtained only measures the number of people who have visited the hospital for treatment. Thus, we can say that the measurements are significantly below the estimates of the total infected population. We gather epidemiological data from the following publicly available data sources: covid19india.org: Coronavirus Outbreak in India () and the Ministry of Health (http://).