The Mathematics Behind Covid-19 and Viral Infections

The book is prepared with three of the most important research works I have completed throughout this year relating to Covid-19. I tried to organize them as clearly and in the most logical order possible, but it is subject to alteration and addition in the future. The first section detailing the cyclic characteristics of Covid-19 diagnoses and its explanation through the infection cycle model. This model can be generalized to explain the stochastic nature and cyclic fluctuation of any epidemic progression. The next section detailing the construction of spatial based simulation model, and the relationships derived based on its simulation. In this section, we focused on a higher layer of abstraction than those typically concerned by SIR/SEIR. That is, we are less concerned about the epidemic progression through time, rather only concerned with the final infection ratio. We are able to show how the final infection ratio can vary by the alteration of different underlying variables such as population density and the freedom of movement. As such, we boldly proposed 6 laws regarding infection. In the last section, we present our method of the prediction for the world regions back in May based on exponentially decreasing regressions on R_{0}. The final validity of the methodology yet to stand the test of time, and many competing prediction methodology, including some of my own, which will be compared with and added later. If one were to assign a level of resolution for epidemic modeling as those used for cartography, then the classic SIR/SEIR model would be a descriptive map of the United States. Our proposed infection cycle model represents the state map, which is at a level of resolution higher. Our spatial simulation model would represent the municipal map, which is at a level of resolution higher still. On the other hand, the 6 laws describing infection ratio can be considered as the world map, with a level of resolution lower than the SIR/SEIR but with a more general view about infection. Therefore, our work attempted to expand the epidemiological studies landscape by introducing 2 level of resolutions higher and 1 level of resolution lower than the current SIR/SEIR model.In 1665, when the great plague ravaged London, Newton retreated to his countryside house, and contemplated hitherto untouched concepts and ideas for the human mind. 355 years later, at the peak of Covid-19, I have also retreated myself to the countryside, contemplating on expanding the scope of existing viral infection model. Newton never made advances in epidemiology, which is understood since the data records at the time were poor. Especially after the Great fire of London that came after the Great Plague definitely destroyed the majority of the records. Living in the midst of abundant computing power and information storage, contemporaries hold an absolute advantage over Newton on interpreting and conceptualizing epidemiology. Therefore, we have little excuses for not able to push the frontier and expand epidemiology. By utilizing my skill and contributing toward the field, at least making the quarantine a more constructive and productive one in the midst of uncertainty.

Author: Steven Suan Zhu

Publisher: Independently Published

Publication Date: 44118

Number of Pages: 294 pages

Binding: Mathematics

ISBN-10:

ISBN-13: 9798696662527