Analyzing pandemic dynamics through traveling waves: a mathematical model

Purpose of research. Pandemic of 2019 has greatly altered human life and affected economies worldwide by increasing death rates. The relevance is understanding and controlling the spread of infections is vital to minimizing its effects. The purpose of the research investigation is to plug spatial dependence into the traditional SIR model to extend its usefulness in modeling the propagation process of the virus. Methods. The methodology is to develop of a mathematical model to represent the pandemic spread as a traveling wave phenomenon. Analysis of the wave speed of the model is made as appropriate as well as the several numerical methods it applied in obtaining solutions. The new variable to the infected population equation is used along with variable transformation techniques and linearization in deriving analytical solutions and then computing and analyzing the wave speed associated with infection spread. Results confirmed the previous outcomes generated by time-dependent models’ analysis that the prime determinant of disease dissemination is the infection-to-recovery rate. It is shown that either transmission coefficient decreases or the recovery rate increases slows down the spread of the disease. Conclusion. As a conclusion, the best possible way to curb its exposure is by minimizing interpersonal interaction (reduction of beta) or by expediting patient recovery and segregation (increase in alpha). It reduces the wave speed parameter q, which controls the rate of propagation of the disease.