Dynamical behavior of a fractional order model of toxoplasmosis infection on a complex heterogeneous network

In this work, a new fractional order model of toxoplasmosis on a complex heterogeneous network is proposed to reflect the interactions between human and cat populations. An analysis of the existence of disease-free and endemic equilibria is presented. In order to evaluate the epidemic threshold, the basic reproduction number is derived from the model. The stability conditions of the disease-free equilibrium point are explored. Numerical examples are performed to simulate different scenarios of the model and to affirm the theoretical analysis. The obtained analytical results indicated that the basic reproduction number can be reduced by decreasing the infection rate of cats, decreasing the loss of immunity rate of cats, enhancing the recovery of cats affected by infection, or increasing the vaccination rate of susceptible cats. Model-predicted health strategies are presented for each scenario to illustrate how the basic reproduction number could be reduced under the model assumptions. These are theoretical predictions and have not been empirically validated. The fractional order parameter and degree of nodes of the complex network effect are explored through the numerical scenarios. Higher fractional order in an endemic environment leads to faster disease spread and earlier peak infections. Lower fractional derivative order results in slower disease propagation, longer peak times, and fewer overall infections. In a disease-free setting, raising the fractional derivative order decreases infection rates quickly. Higher infection levels are observed when the nodes degrees are increased. To improve the model’s practical usefulness, we parameterized it using evidence-informed values derived from real epidemiological data. The parameterized model produces dynamics qualitatively consistent with field observations, demonstrating the validity of the theoretical framework.