A delayed Schistosomiasis transmission model and its dynamics

Abstract

A 6-dimension dynamical Schistosomiasis model incorporating 5 time delays is established in order to investigate the effects of time delays on the transmission mechanisms of Schistosomiasis. The stability behaviors at the endemic equilibrium are presented under different cases, which relate to the threshold value for disease breakout. The following results and available control strategies can be obtained from theoretical analyses and numerical simulations. (1) The incubation of egg hatching can postpone the outbreak of Schistosomiasis. Therefore it can be used as a new method for the control of Schistosomiasis spread that prolonging the incubation of egg hatching. (2) The time delays in miracidia and cercaria can extend the disease transmission cycle. Thus lengthening the incubation periods in miracidia and cercaria can be beneficial to Schistosomiasis prevention at the beginning. (3) The maturation periods of schistosome and sporocyst could give rise to Hopf bifurcations and periodic orbits, respectively, and the basic reproductive number decreases with respect to the maturation of sporocyst. Therefore, it is a reasonable strategy to control the spread of Schistosomiasis that prolonging the maturation duration of the sporocyst in snails. The consequences obtained motivate us that we can choose the right time to do the control laws, such as in winter (when lower temperature).