Abstract
Mathematical modeling is an effective tool for understanding and predicting certain endemic diseases. Toxoplasmosis gondii (T. gondii) is an endemic disease that is transmitted to human by contact with infected cats. T. gondii can cause a lot of diseases in human body and also affects the human body parts. In this study we have constructed a mathematical model to understand the transmission and control of this disease by utilizing the harmonic mean-type incidence rate which is more effect 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.