solving ordinary differential equations meetings are effective in the sense that the susceptible actually becomes infected counting that people get infected in such pairwise meetings (say are infected from meetings)we can estimate the probability of being infected as = the expected number of individuals in the category that in time interval catch the virus and get infected is then tsi introducing new constant pto save some writingwe arrive at the formula vtsi the value of must be known in order to predict the future with the disease model one possibility is to estimate and from their meanings in the derivation above alternativelywe can observe an "experimentwhere there are susceptibles and infected at some point in time during time interval we count that susceptibles have become infected using ( as rough approximation of how has developed during time (and now is not necessarily smallbut we use ( anyway)we get ( vt we need an additional equation to describe the evolution of tsuch an equation is easy to establish by noting that the loss in the category is corresponding gain in the category more preciselyi nc vts ( howeverthere is also loss in the category because people recover from the disease suppose that we can measure that out of individuals recover in time period (say of sick people recover during daym hnowd mnt is the probability that one individual recovers in unit time interval then (on averageti infected will recover in time interval this quantity represents loss in the category and gain in the category we can therefore write the total change in the category as nc vts ti ( the change in the category is simplethere is always an increase from the categoryrnc rn ti ( since there is no loss in the category (people are either recovered and immuneor dead)we are done with the modeling of this category in factwe do not strictly need the equation ( for rbut extensions of the model later will need an equation for dividing by in ( and ( and letting results in the corresponding differential equations and vsi ( ( to summarizewe have derived difference equations ( )-( )and alternative differential equations ( )-( for referencewe list the complete set of the