Consider the spreading of COVID19 on an isolated South African village with population size 12 000. A portion of the population travels to nearest city for work and shopping and returns to the village infected with the disease. You would like to predict the number of the people I who will have been infected by some time t (days). Consider the following model dI/dt = 0.05I(12000 − I)      I(0) = 10. (a) Solve the model for I as a function of t. (b) Determine the time T3 needed for one-third of the population to be infected.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.