to summarizethe spreading of this disease is essentially the dynamics of moving individuals from the to the and then to the categorywe can use mathematics to more precisely describe the exchange between the categories the fundamental idea is to describe the changes that take place during small time intervaldenoted by our disease model is often referred to as compartment modelwhere quantities are shuffled between compartments (here synonym for categoriesaccording to some rules the rules express changes in small time interval tand from these changes we can let go to zero and obtain derivatives the resulting equations then go from difference equations (with finite tto differential equations ( we introduce uniform mesh in timetn ntn and seek at the mesh points the numerical approximation to at time tn is denoted by similarlywe seek the unknown values of tand tat the mesh points and introduce similar notation and rn for the approximations to the exact values tn and tn in the time interval we know that some people will be infectedso will decrease we shall soon argue by mathematics that there will be vtsi new infected individuals in this time intervalwhere is parameter reflecting how easy people get infected during time interval of unit length if the loss in is vtsi we have that the change in is nc vts ( dividing by and letting makes the left-hand side approach tn such that we obtain differential equation vsi ( the reasoning in going from the difference equation ( to the differential equation ( follows exactly the steps explained in sect before proceeding with how and develops in timelet us explain the formula vtsi we have susceptibles and infected people these can make up si pairs nowsuppose that during time interval we measure that actual pairwise meetings do occur among theoretically possible pairings of people from the and categories the probability that people meet in pairs during time is (by the empirical frequency definition of probabilityequal to =ni the number of successes divided by the number of possible outcomes from such statistics we normally derive quantities expressed per unit timei here we want the probability per unit timewhich is found from dividing by mnt given the probability the expected number of meetings per time interval of si possible pairs of people is (from basic statisticssi during time interval tthere will be sit expected number of meetings between susceptibles and infected people such that the virus may spread only fraction of the tsi