Transmission Dynamics of COVID-19 and Impact on Public Health Policy

B Shayak; Mohit Manoj Sharma; Richard H Rand; Awadhesh Kumar Singh; Anoop Misra

We shall now solve the model for some test cases to demonstrate its plausibility. We measure time in days, from t = 0 to t = 100, at which point we assume that the epidemic is over (for example through change in temperature, mutation of the virus, development of a cure etc). We use the time step h = 0.001 day. We assume that the population of the region is 500 units (for the plots we shall normalize to unity but for the simulation, a larger number proved convenient). The benchmark parameter values we consider are k0 = k3 = 0.0008, k4 = 0.0004, μ1 = 0.18, μ2 = 0.02, and the delays τ1 = 7, τ2 = 3 and τ3 = 5 (we shall explain some of the choices later). A delay differential equation needs to be seeded with initial functions lasting as long as the maximum delay involved in the problem. Here, this maximum is 15. So we have gone with the initial functions x (t) = 500 − t/15, y (t) = t/15, z (t) = 0 and w (t) = 2 x 10 −6 for the time interval [0, 15] . This assumes a slow growth of the epidemic during the seeding period. The time traces of x, y, z and w for this run are shown in the Figure below. Here and henceforth, we plot x in blue, y in green, z in red and w in grey. In the rate plots which appear later, we shall use the same colour scheme for the time derivatives of these four variables. We also normalize the initial population to unity. The results are physically plausible with the number of healthy at large people (blue) decreasing over time and the various other populations increasing over time. Before proceeding further, we briefly comment on the parameter values for this run. The values of τ1, τ2 and μ1 come from virological studies and are approximately independent of region. For τ2, Reference [43] reports that patients admitted to hospital with COVID-19 already carried significant viral loads. Since the median incubation period for COVID-19 estimated there and elsewhere [16] is about 5 days, we have taken τ2 to be 3 days, or approximately half . CC-BY-NC 4.0 International license It is made available under a preprint in perpetuity.