On an Sir Epidemic Model for the COVID-19 Pandemic and the Logistic Equation
Algorithm 1
Evaluation of the Malthusian parameter and the carrying capacity.
(1)
Step 0: Choose and the initial intervention Phase to start to run the procedure.
(2)
Smooth the recorded infection curve , if the recorded data are discrete, to make the amended one defined everywhere since the logistic equation used for modelling is continuous through time.
(3)
Define for and to then run (53)–(55) to generate the sequences and of sampling instants and inter-sampling intervals (or sampling periods) with being small enough for the local time-invariance parameterization of the logistic equation to work efficiently.
(4)
Step 1: Given the current sampling instant , locate the intervention phase to which it belongs. Calculate the inter-sampling interval via (54) and some of the equations (55)–(57) and then calculate the next sampling instant
(5)
Step 2: Read from recorded data
(6)
Step 3: The Malthusian parameter and the carrying capacity at time are calculated “a posteriori” at time from the registered , and evaluated at the current and next time instants and and an “a priori” estimation of from equations (A.12)–(A.14) and (A.5) in Appendix A (Remark A.1).
Step 5: If then make and GoTo Step 1. Else GoTo Step 6
(9)
Step 6: Calculate the average disease transmission rate of the Phase , make and if the whole number of checked phases is unfinished GoTo Step 1. Else GoTo Step 7
