Stochastic Modelling of the Impact of Asymptomatic Infection and the Use of Non-COVID-19 Drugs on COVID-19 Dynamics

Abstract

We present a stochastic epidemic model for studying the dynamics of COVID-19, which takes into account asymptomatic infections and the use of non-COVID-19 drugs. This stochastic model is formulated as a continuous-time Markov chain (CTMC), based on assumptions underlying its deterministic counterpart. Both the analytical and numerical results highlight notable differences in predictions and long-term behavior between stochastic and deterministic models, which are essential for preventing disease outbreaks. The probability of disease extinction derived from the branching processes aligns closely with numerical simulation results. Our findings indicate a high likelihood of disease extinction when outbreaks originate from symptomatic infectious individuals, whereas epidemics initiated by asymptomatic infectious individuals yield the lowest probabilities. By considering 10,000 sample paths, we estimate how long it takes for the disease to disappear; the results indicate that the disease lasts the shortest time when it starts with symptomatic individuals and the longest when all three types of infectious individuals are involved from the beginning. Additionally, numerical simulations demonstrate that increased use of non-COVID-19 drugs to manage symptoms in COVID-19 patients generally enhances the probability of disease extinction.