Since the unfortunate appearance of COVID-19, there has been a massive number of mathematical models based on the SIR or SEIR models. A perusal of these has shown that the models are mainly numerical simulations to predict the course of the outbreak under varying conditions. Would an understanding of the disease dynamics be improved if equilibria or bifurcation analysis was incorporated?
Yes I have a work were these analysis was incorporated. So its possible. Though the work is still under review but I have uploaded it as preprint for others to read.
I think yes, an understanding of the disease dynamics be improved if equilibria or bifurcation analysis was incorporated.
Yes, but it is not the best solution. Considering that with the development of the epidemic, the virulence of the epidemic process changes, the rules for its spreading also change. Therefore, the best way to study the dynamics of the epidemic process of COVID-19 is not SIR-models based on differential equations, since making changes to them is extremely difficult. In my opinion, an agent-based approach is optimal for conducting virtual experiments to understand the behavior of the epidemic process.
@ Dmytro Chumachenko
Both types of approaches have their strengths and weaknesses. I love the versatility of compartmental models. They can be also be easily modified as information about the characteristics of disease transmission changes. For instance, initially asymptomatic transmission (where individuals are infected but display no symptoms) was thought to be rare – the SIR model was then updated with the addition of acompartment of asymptomatic infected people/carriers A to form a SEIRA model.
I believe that compartmental models are a good initial approach to get an idea of the underlying dynamics then they may be refined with the agent based models.