Insights from Atangana-Baleanu fractional derivatives modeling of influenza epidemics and sensitivity analysis.

Mathematical modeling is an effective tool for understanding and predicting certain endemic diseases. Influenza is a common endemic disease that is transmitted to humans by contact with infected humans. During winter, seasonal influenza occurs annually in all ages causing fever and other diseases. In this study, we have constructed a mathematical model to understand the transmission of this disease by utilizing the harmonic mean-type incidence rate which is more effective than other incidence rates. We calculated the disease-free equilibria, endemic equilibria and then basic reproduction number which is important to understand the disease reduction from the population. Sensitivity analysis of reproduction number presents the effect of parameters on disease transmission. To generalize the traditional integer-order model to a fractional framework, the Atangana-Baleanu fractional-order derivative is employed. The fractionalized model is both existent and unique. The fractional version of the proposed model is numerically analyzed using the Atangana-Toufik method. Results present that by increasing the value of the treatment rate, there is a decline in the disease in the population.