New approximations, and policy implications, from a delayed dynamic model of a fast pandemic

Chandrika Prakash Vyasarayani; Anindya Chatterjee

In the above, if β was constant rather than time-varying, then its t-dependence would be dropped. Note that, if β varies with time, its variation can be considered externally specified and not a part of the solution. Equations (7) and (8) make intuitive sense in a lumped-variable setting as follows. Equation (7) says that the instantaneous rate of new infections is proportional to how infectious the disease is (β), how much people are meeting each other (m(t)), how many uninfected people there are (S(t)) and how many infectious people are out in public (I(t)). Equation (8) says that the rate of change in the number of infectious people is equal to previously infected people just exiting the latency phase and entering the infectious phase, minus the rate at which people are recovering on their own, minus also the rate at which people displaying symptoms are being put into quarantine (these quarantined people are slightly diminished in number due to self-recovery, which is good; and due to some people not being quarantined, which is a system inefficiency). We are interested in near-unity initial conditions for S(−∞) = 1 that lead to growth of the infection and eventual saturation. In particular, the net damage done by the disease is represented by 1 − S(∞).