A fractional measles model having monotonic real statistical data for constant transmission rate of the disease

Non-Markovian effects have a vital role in modeling the processes related with natural phenomena such as epidemiology. Various infectious diseases have long-range memory characteristics and, thus, non-local operators are one of the best choices to be used to understand the transmission dynamics of such diseases and epidemics. In this paper, we study a fractional order epidemiological model of measles. Some relevant features, such as well-posedness and stability of the underlying Cauchy problem, are considered accompanying the proofs for a locally asymptotically stable equilibrium point for basic reproduction number R0 < 1, which is most sensitive to the fractional order parameter and to the percentage of vaccination. We show the efficiency of the model through a real life application of the spread of the epidemic in Pakistan, comparing the fractional and classical models, while assuming constant transmission rate of the epidemic with monotonically increasing and decreasing behavior of the infected population. Secondly, the fractional Caputo type model, based upon nonlinear least squares curve fitting technique, is found to have smaller residuals when compared with the classical model.publishe

Solution of an SEIR Epidemic Model in Fractional Order

In this paper, we consider the SEIR (Susceptible-Exposed-Infected-Recovered) epidemic model (with out of bilinear incidence rates) in fractional order. First the non-negative solution of the SEIR model in fractional order is discussed. Then calculate an approximate solution of the proposed model. The obtained results are compaired with those obtained by forth order Runge-Kutta method and nonstandard numerical method in the integer case. Finally, we present some numerical results

Synchronization of a class of fractional-order neural networks with multiple time delays by comparison principles

This paper studies the synchronization of fractional-order neural networks with multiple time delays. Based on an inequality of fractional-order and comparison principles of linear fractional equation with multiple time delays, some sufficient conditions for synchronization of master-slave systems are obtained. Example and related simulations are given to demonstrate the feasibility of the theoretical results

The Fractional SIRC Model and Influenza A

This paper deals with the fractional-order SIRC model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, 0. We give a detailed analysis for the asymptotic stability of disease-free and positive fixed points. Nonstandard finite difference methods have been used to solve and simulate the system of differential equations

On Local Asymptotic Stability of q-Fractional Nonlinear Dynamical Systems

In this paper, locally asymptotic stability of q-fractional order nonlinear dynamical systems is introduced and studied. The sufficient conditions for local stability of such dynamical systems are obtained. Also, useful definitions of fractional order q-integrals and q-derivatives are recalled. Finally, a q-fractional order nonlinear dynamical model is considered