چكيده به لاتين
Abstract:
In this thesis, some mathematical models of infectious diseases, including infectious
diseases, SIRS, Dengue Fever and Cholera, have been analyzed from an analytical
point of view, and with the development of previous models an optimized mathematical
model has been introduced by adding some possible parameters.
The first proposed mathematical model for infectious diseases, SIRS, is the parameter
that is included in the variable function model in terms of time, which is adapted
to the actual outbreak model and therefore has a better performance than the previous
models. We show that under positive initial conditions, the response of the device is
positive, as well as the stable asymptotic alternate response. The model is simulated
by the fourth-order Runge-Kotta method.
The second presented mathematical model is related to the prevalence of Dengue Fever,
which is modeled as a system of nonlinear differential equations between human populations
and mosquitoes. From theoretical and analytical point of view, the answer of
the above model has been studied with respect to positive initial conditions in a time
boundary interval.
Finally, the last mathematical model discussed in this dissertation is related to the outbreak
of Cholera. It is a mathematical model of fractional derivatives in the presence
of some control parameters such as vaccination, treatment and water sanitation. The
equilibrium points and local stability of these equilibrium points have been investigated
according to the basic reproductive number R0 and we have shown that R0 plays an
important role in the prevalence and control of Cholera.
