A fractional mathematical model to represent the spread of two different epidemics by vertical transmission

In this thesis, epidemic diseases with vertical transmission and a vertical transmission model that takes this disease into account are considered. In this vertical transmission model, the behaviour of such models has been studied by replacing the classical derivative with fractional derivatives such as Caputo, Caputo-Fabrizio and Atangana-Baleanu. The vertical transmission model with fractional derivatives is solved numerically using a method based on the Lagrange polynomial. Moreover, by using the newly introduced concept of piecewise differential equations, a new model has been created in which another vertical transmission is included in a population where, after a while, there is vertical transmission. Different situations of these models, whose different patterns are presented, are considered and the numerical simulations obtained for these patterns are presented with graphical representations.