The Dynamics of Growing Islets and Transmission of Schistosomiasis Japonica in the Yangtze River

Abstract

We formulate and analyze a system of ordinary differential equations for the transmission of schistosomiasis japonica on the islets in the Yangtze River, China. The impact of growing islets on the spread of schistosomiasis is investigated by the bifurcation analysis. Using the projection technique developed by Hassard, Kazarinoff and Wan, the normal form of the cusp bifurcation of codimension 2 is derived to overcome the technical difficulties in studying the existence, stability, and bifurcation of the multiple endemic equilibria in high-dimensional phase space. We show that the model can also undergo transcritical bifurcations, saddle-node bifurcations, a pitchfork bifurcation, and Hopf bifurcations. The bifurcation diagrams and epidemiological interpretations are given. We conclude that when the islet reaches a critical size, the transmission cycle of the schistosomiasis japonica between wild rats Rattus norvegicus and snails Oncomelania hupensis could be established, which serves as a possible source of schistosomiasis transmission along the Yangtze River.

Fine scale Spatial-temporal cluster analysis for the infection risk of Schistosomiasis japonica using space-time scan statistics

“…Anhui province was known as a schistosomiasis endemic hotspot in the past, this could be attributed to the varying complexity in the geographic landscape of the entire region and the interplay between human activities, cattle and vector snails that are important components in the epidemiology of the disease [ 7 , 23 ]. This complexity has enhanced the transmission of schistosomiasis in the region and also makes control strategies targeted at eliminating this debilitating disease in the region difficult to be effectively implemented [ 29 , 30 ]. However, should information on spatial and temporal clustering pattern of schistosomiasis infection in Anhui province be provided, future control strategies would be effectively implemented owing to the adequate background knowledge available [ 31 ].…”

The influence of natural factors on the spatio-temporal distribution of Oncomelania hupensis

“…Compared with the eastern region relatively far from the lake, the lake region is crisscrossed by irrigation canals and ditches, and resident production and living activities are frequent, making the schistosomiasis prevalence in the region more serious, which is why it has attracted increasing attention from relevant departments. Therefore, snail density changes may objectively be caused by some local environmental differences, such as channel type; weed density and man-made factors, including agricultural and pastoral activities; snail control projects; and so on (Qiu et al, 2014;Shan et al, 2014). Of course, the specific mechanisms underlying these changes require more research and validation.…”

A schistosomiasis compartment model with incubation and its optimal control

“…The first model of schistosomiasis was proposed by Macdonald in 1965 . And then, there have been more mathematical models to exploit the transmission dynamical mechanism of schistosomiasis from different perspectives, such as density dependence and age structure , bifurcation , seasonal variation , parameters estimation , multi‐hosts , and so on. The papers mentioned earlier are all ordinary differential equations (ODE).…”