Mathematical modeling has proved to be an essential tool for the development of control strategies and distinguishing the determinants of dynamics of the disease. A key determinant of a given potential of a model to help with such measurements is the availability of data to parameterize the model. For developing countries in particular, data are often scarce and difficult to collect. It is therefore important to understand the types of data needed for a successful modeling project. Infectious diseases are a persistent problem worldwide, potentially threatening all those who get in touch with them. This thesis attempts to improve our understanding of infectious diseases by develop mathematical models for cellular dynamics of human infectious diseases. This was achieved through the investigation of interaction between infectious agents and cells of humoral and cell-mediated immune response. In this thesis, we look at different types of models such as measles, HIV , dengue, SIR and diabetes. Sensitivity analysis of these models are provided by threshold and number of reproductions (i.e reproductive number), as well as analyzed qualitatively and also check the stability analysis of these models. A nonlinear mathematical model is used to study and evaluate the dynamics of measles, HIV, diabetic dengue and its impact on public health in the community. we developed a non-standard finite difference scheme by applying the Micken approach f(h) = h+O(h2) instead of h to control the spread of bad impact of diseases in society, which is dynamically consistent, easy to implement, converges unconditionally and shows a good agreement to control the harmful effects of diseases in our population that are causes of death. Numerical simulations are also established to explore the effect of system parameters on the propagation of the disease. In this thesis we propose a fractional order model to describe the dynamics of human immunodeficiency virus (HIV) infection. A nonlinear time fractional model is used in order to understand the outbreaks of this epidemic diseases. Verify the non-negative unique solution of the developed fractional order models. The Caputo fractional derivative operator of order ae(0;1] is employed to obtain the fractional differential equations. Laplace adomian decomposition method has been employed to solve these fractional order models. Finally, some numerical results presented show the effect of the fractional parameters a and f on our solutions obtained.Finally, some numerical results presented show the effect of the fractional parameters a and f on our solutions obtained. The LADM is applied to give an approximate solution of nonlinear fractional ordinary differential equation system of models with different fractional values.