An Evolutionary Theory on Virus Mutation in COVID-19 (preprint)

With the rapid evolution of SARS-CoV-2, the emergence of new strains is an intriguing question. This paper presents an evolutionary theory to analyze the mutations of the virus and identify the conditions that lead to the generation of new strains. We represent the virus variants using a 4-letter sequence based on amino acid mutations on the spike protein and employ an n-distance algorithm to derive a variant phylogenetic tree. We show that the theoretically-derived tree aligns with experimental data on virus evolution. Additionally, we propose an A-X model, utilizing the set of existing mutation sites (A) and a set of randomly generated sites (X), to calculate the emergence of new strains. Our findings demonstrate that a sufficient number of random iterations can predict the generation of new macro-lineages when the number of sites in X is large enough. These results provide a crucial theoretical basis for understanding the evolution of SARS-CoV-2.

Mathematical Modelling of Virus Spreading in COVID-19 (preprint)

A mathematical model is proposed to analyze the spreading dynamics of COVID-19. By using the parameters of the model, namely the basic reproduction number (R0) and the attenuation constant (k), the daily number of infections (DNI) and the cumulative number of infections (CNI) are deduced and shown to be in good agreement with experimental data. This model effectively addresses three key issues: explaining the waveform pattern of DNI, predicting the occurrence of the second wave of infection, and understanding the competitive spread of two viruses in a region. The findings demonstrate that these significant challenges can be comprehensively tackled using a simple mathematical framework. The theoretical insights derived from this model hold potential in guiding the estimation of the severity of an infection wave and formulating effective strategies for the control and mitigation of epidemic outbreaks.

Spike conformation transition in SARS-CoV-2 infection (preprint)

A theory on the conformation transition for SARS-CoV-2 spike protein (S) is established. The conformation equilibrium between open (up) and closed (down) conformations of receptor binding domain (RBD) is studied from the first-principle. The free energy change in conformation transition of S protein is introduced and we demonstrated that it includes two parts, one from the difference of conformation potential and another from the variation of structural elasticity. The latter is dependent of amino acid mutation. When the amino acid mutation of S protein causes a substantial reduction of elastic energy the equilibrium is biased to the open conformation. Only then can the virus infection process continue. That both the D614G mutation and the K986P mutation increase the COVID-19 infectivity and why a large number of mutations, including those at interface residues, have not been selected in current SARS-CoV-2 pandemic are interpreted from the presented theory. The evolution of coronavirus dependent on the alteration of conformation equilibrium is indicated. Finally, introduction of electric field to change the conformation potential barrier and how the conformation equilibrium depends on temperature and humidity are briefly discussed.

Phylogenetic study of 2019-nCoV by using alignment-free method (preprint)

The origin and early spread of 2019-nCoV is studied by phylogenetic analysis using IC-PIC alignment-free method based on DNA/RNA sequence information correlation (IC) and partial information correlation (PIC). The topology of phylogenetic tree of Betacoronavirus is remarkably consistent with biologist's systematics, classifies 2019-nCoV as Sarbecovirus of Betacoronavirus and supports the assumption that these novel viruses are of bat origin with pangolin as one of the possible intermediate hosts. The novel virus branch of phylogenetic tree shows location-virus linkage. The placement of root of the early 2019-nCoV tree is studied carefully in Neighbor Joining consensus algorithm by introducing different out-groups (Bat-related coronaviruses, Pangolin coronaviruses and HIV viruses etc.) and comparing with UPGMA consensus trees. Several oldest branches (lineages) of the 2019-nCoV tree are deduced that means the COVID-19 may begin to spread in several regions in the world before its outbreak in Wuhan.