As most communicable diseases, schistosomiasis transmission mechanism involves some
delay due to the incubation period. In this study, we seek to investigate the impact of incubation
period on schistosomiasis global transmission dynamics. For that, starting from our previous
work and using delay differential equations, we have proposed a more sophisticated model
in which the new feature we accounted is the latency period in both human and snail hosts.
Then, under some suitable assumptions, the mathematical analysis of the model has been
done. Specifically, we calculated the basic reproduction number and showed its dependence
on the delays in both humans and snails as follows: when the delays in humans and snails
increase, R0 decreases. We also proved that when R0 1, the system is uniformly persistent and admits
a unique endemic equilibrium. Besides, by formulating a suitable Lyapunov function, we
established that the unique endemic steady state of the model is globally asymptotically
stable when the threshold parameter R0 exceeds 1. Furthermore, sensitivity analysis has
been carried out to show how parameters variations affect the model global behaviour. We
finished by illustrating some numerical results that are well in keeping with our theoretical
findings.

Mathematical analysis, Schistosomiasis transmission, Incubation period, Basic reproduction number, General incidence functions, Delay differential equations, Numerical simulations