solving ordinary differential equations outbreak or not looking at the equation for it is clear that we must have vsi for to increase when we start the simulation it means that vs / or simpler vs > ( to increase the number of infected people and accelerate the spreading of the disease you can run the sir py program with smaller such that ( is violated and observe that there is no outbreak the power of mathematical modeling the reader should notice our careful use of words in the previous paragraphs we started out with modeling very specific casenamely the spreading of flu among pupils and staff at boarding school with purpose we exchanged words like pupils and flu with more neutral and general words like individuals and diseaserespectively phrased equivalentlywe raised the abstraction level by moving from specific case (flu at boarding schoolto more general case (disease in closed societyvery oftenwhen developing mathematical modelswe start with specific example and seethrough the modelingthat what is going on of essence in this example also will take place in many similar problem settings we try to incorporate this generalization in the model so that the model has much wider application area than what we aimed at in the beginning this is the very power of mathematical modelingby solving one specific case we have often developed more generic tools that can readily be applied to solve seemingly different problems the next sections will give substance to this assertion abstract problem and notation when we had specific differential equation with one unknownwe quickly turned to an abstract differential equation written in the generic form utwe refer to such problem as scalar ode specific equation corresponds to specific choice of the formula utinvolving and (optionallyt it is advantageous to also write system of differential equations in the same abstract notationu ut/but this time it is understood that is vector of functions and is also vector we say that utis vector ode or system of odes in this case for the sir model we introduce the two -vectorsone for the unknownsu / / //