Modeling the transmission phenomena of water-borne disease with non-singular and non-local kernel

Drinking or recreating water that has been polluted with disease-causing organisms or pathogens is what causes waterborne infections. It should be noted that many water-borne infections can also transmit from person to person, by contact with animals or their surroundings, or by ingesting tainted food or beverages. Schistosomiasis is a water-borne infection found in different areas of the globe. Mostly people with this viral infection live in Africa with limited resources and medications. Therefore, investigation of this infection is significant to reduce its economic burden on the society. We formulated a novel epidemic model for schistosomiasis water-borne infection with the help of the Atangana–Baleanu derivative. The rudimentary theory of fractional-calculus has been presented for the analysis of our system. We start by looking at the model solution’s non-negativity and uniqueness. The basic reproduction number and equilibria of the hypothesized water-borne infection model are next evaluated. Local stability of the infection-free steady-state has been established through Jacobian matrix method for R0<1. In addition, the suggested model’s solution is calculated using an iterative technique. Finally, we give numerical simulations for various input values to illustrate the impact of memory index and other input factors of the system. Our findings showed the influence of input parameters on the dynamical behaviour of the schistosomiasis infection. The results demonstrate the importance and persuasive behaviour of fractional order, and reveal that fractional memory effects in the model seem to be a good fit for this type of findings.