Numerical study of an influenza epidemic model with diffusion

A diffusive epidemic model is investigated with a view to describe the transmission of influenza as an epidemic. The equations are solved numerically using the splitting method under different initial distribution of population density. It is shown that the initial population distribution and diffusion play an important role for spread of disease. It is also shown that interventions (medical and nonmedical) significantly slow down the spread of disease. Stability of equilibria of the numerical solutions are also established

The generalized Kudryashov method to obtain exact traveling wave solutions of the PHI-four equation and the Fisher equation

In recent years, searching exact traveling wave solutions to nonlinear evolution equations (NLEEs) has become a remarkable topic of research. In this article, we obtain exact traveling wave solutions of two significant NLEEs, namely, the PHI-four equation and the Fisher equation involving parameters by using the generalized Kudryashov method. We attain some exponential type solutions including kink soliton, bisymmetry soliton, and periodic solution when the parameters receive different values. We provide the graphical representations of the respective solutions also. Keywords: NLEEs, generalized Kudryashov method, PHI-four equation, Fisher equation, Traveling wave solution

Uncertainty and sensitivity analysis of the basic reproduction number of a vaccinated epidemic model of influenza

The basic reproduction number and the point of endemic equilibrium are two very important factors in any deterministic compartmental epidemic model as the basic reproduction number and the point of endemic equilibrium represent the nature of disease transmission and disease prevalence respectively. In this article the sensitivity analysis based on mathematical as well as statistical techniques has been performed to determine the importance of the epidemic model parameters. It is observed that 6 out of the 11 input parameters play a prominent role in determining the magnitude of the basic reproduction number. It is shown that the basic reproduction number is the most sensitive to the transmission rate of disease. It is also shown that control of transmission rate and recovery rate of the clinically ill are crucial to stop the spreading of influenza epidemics

A numerical study on an influenza epidemic model with vaccination and diffusion

A vaccinated diffusive compartmental epidemic model is developed to explore the impact of vaccination as well as diffusion on the transmission dynamics of influenza. The basic reproduction numbers with and without vaccination are obtained. Sensitivity analysis of the reproduction number based on parameters involved in the system has been investigated. Stability analysis of the points of equilibrium has also been investigated. Using the combined effect of the vaccine efficacy and vaccination rate, the model is analysed to determine criteria for control of influenza epidemic. The roles of vaccine efficacy and vaccination rate are compared. It is shown that higher levels of vaccine efficacy and vaccination rate lead to a decrease in the epidemic size. It is also shown that an accurate estimation of the efficiency of vaccine is necessary to control the spread of influenza and thus vaccination strategy needs to be implemented carefully

Parameter estimation of influenza epidemic model

SEIRS and SVEIRS epidemic models are considered here to capture the main characteristic of transmission of influenza epidemic governed by a system of differential equations. All parameters estimations involved in these models are based on the influenza epidemic which occurred in Australia in 1919, often called Spanish flu data Sydney. Least squares method, which involves minimization of the sum of squared differences between the measurements and the model predictions is used to estimate the unknown parameters for both models. Graphical as well as numerical methods are used to validate these models. It is shown that our models reflect considerably the dynamical behavior of the influenza epidemic field data used. An important view of the disease dynamics including vaccine efficacy and level of vaccination is also drawn