A systematic approach for COVID-19 predictions and parameter estimation.

The world is currently facing a pandemic called COVID-19 which has drastically changed our human lifestyle, affecting it badly. The lifestyle and the thought processes of every individual have changed with the current situation. This situation was unpredictable, and it contains a lot of uncertainties. In this paper, the authors have attempted to predict and analyze the disease along with its related issues to determine the maximum number of infected people, the speed of spread, and most importantly, its evaluation using a model-based parameter estimation method. In this research the Susceptible-Infectious-Recovered model with different conditions has been used for the analysis of COVID-19. The effects of lockdown, the light switch method, and parameter variations like contact ratio and reproduction number are also analyzed. The authors have attempted to study and predict the lockdown effect, particularly in India in terms of infected and recovered numbers, which show substantial improvement. A disease-free endemic stability analysis using Lyapunov and LaSalle's method is presented, and novel methods such as the convalescent plasma method and the Who Acquires Infection From Whom method are also discussed, as they are considered to be useful in flattening the curve of COVID-19.

Prediction of Epidemics Trend of COVID-19 in Bangladesh.

Background: Amid a critical and emergent situation like the coronavirus disease (COVID-19) pandemic related to extreme health and economic repercussions, we used and presented the mathematical modeling like susceptible-infectious-recovered (SIR) to have a numerical demonstration that can shed light to decide the fate of the scourge in Bangladesh. To describe the idea about the factors influencing the outbreak data, we presented the current situation of the COVID-19 outbreak with graphical trends. Methods: Primary data were collected and analyzed by using a pre-created Google Survey form having a pre-set questionnaire on the social distancing status of different districts. Secondary data on the total and the daily number of laboratory tests, confirmed positive cases, and death cases were extracted from the publicly available sources to make predictions. We estimated the basic reproduction number (R◦) based on the SIR mathematical model and predicted the probable fate of this pandemic in Bangladesh. Results: Quarantine situations in different regions of Bangladesh were evaluated and presented. We also provided tentative forecasts until 31 May 2020 and found that the predicted curve followed the actual curve approximately. Estimated R◦-values (6.924) indicated that infection rate would be greater than the recovery rate. Furthermore, by calibrating the parameters of the SIR model to fit the reported data, we assume the ultimate ending of the pandemic in Bangladesh by December 2022. Conclusion: We hope that the results of our analysis could contribute to the elucidation of critical aspects of this outbreak and help the concerned authority toward decision making.

Population agglomeration is a harbinger of the spatial complexity of COVID-19.

The spatial template over which COVID-19 infections operate is a result of nested societal decisions involving complex political and epidemiological processes at a broad range of spatial scales. It is characterized by 'hotspots' of high infections interspersed within regions where infections are sporadic to absent. In this work, the sparseness of COVID-19 infections and their time variations were analyzed across the US at scales ranging from 10 km (county scale) to 2600 km (continental scale). It was found that COVID-19 cases are multi-scaling with a multifractality kernel that monotonically approached that of the underlying population. The spatial correlation of infections between counties increased rapidly in March 2020; that rise continued but at a slower pace subsequently, trending towards the spatial correlation of the population agglomeration. This shows that the disease had already spread across the USA in early March such that travel restriction thereafter (starting on March 15th 2020) had minor impact on the subsequent spatial propagation of COVID-19. The ramifications of targeted interventions on spatial patterns of new infections were explored using the epidemiological susceptible-infectious-recovered (SIR) model mapped onto the population agglomeration template. These revealed that re-opening rural areas would have a smaller impact on the spread and evolution of the disease than re-opening urban (dense) centers which would disturb the system for months. This study provided a novel way for interpreting the spatial spread of COVID-19, along with a practical approach (multifractals/SIR/spectral slope) that could be employed to capture the variability and intermittency at all scales while maintaining the spatial structure.