ABSTRACT
Mathematical models have assisted in describing the transmission and propagation dynamics of various viral diseases like MERS, measles, SARS, and Influenza; while the advanced computational technique is utilized in the epidemiology of viral diseases to examine and estimate the influences of interventions and vaccinations. In March 2020, the World Health Organization (WHO) has declared the COVID-19 as a global pandemic and the rate of morbidity and mortality triggers unprecedented public health crises throughout the world. The mathematical models can assist in improving the interventions, key transmission parameters, public health agencies, and countermeasures to mitigate this pandemic. Besides, the mathematical models were also used to examine the characteristics of epidemiological and the understanding of the complex transmission mechanism. Our literature study found that there were still some challenges in mathematical modeling for the case of ecology, genetics, microbiology, and pathology pose; also, some aspects like political and societal issues and cultural and ethical standards are hard to be characterized. Here, the recent mathematical models about COVID-19 and their prominent features, applications, limitations, and future perspective are discussed and reviewed. This review can assist in further improvement of mathematical models that will consider the current challenges of viral diseases.
ABSTRACT
In this work, the partitioning clustering of COVID-19 data using c-Means (cM) and Fuzy c-Means (Fc-M) algorithms is carried out. Based on the data available from January 2020 with respect to location, i.e., longitude and latitude of the globe, the confirmed daily cases, recoveries, and deaths are clustered. In the analysis, the maximum cluster size is treated as a variable and is varied from 5 to 50 in both algorithms to find out an optimum number. The performance and validity indices of the clusters formed are analyzed to assess the quality of clusters. The validity indices to understand all the COVID-19 clusters' quality are analysed based on the Zahid SC (Separation Compaction) index, Xie-Beni Index, Fukuyama-Sugeno Index, Validity function, PC (performance coefficient), and CE (entropy) indexes. The analysis results pointed out that five clusters were identified as a major centroid where the pandemic looks concentrated. Additionally, the observations revealed that mainly the pandemic is distributed easily at any global location, and there are several centroids of COVID-19, which primarily act as epicentres. However, the three main COVID-19 clusters identified are 1) cases with value <50,000, 2) cases with a value between 0.1 million to 2 million, and 3) cases above 2 million. These centroids are located in the US, Brazil, and India, where the rest of the small clusters of the pandemic look oriented. Furthermore, the Fc-M technique seems to provide a much better cluster than the c-M algorithm.