Open AccessMulti-host transmission dynamics of schistosomiasis and its optimal control
Author(s) -
Changhong Ding,
Zhipeng Qiu,
Huaiping Zhu
Publication year - 2015
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2015.12.983
Subject(s) - schistosomiasis , transmission (telecommunications) , constant (computer programming) , stability theory , basic reproduction number , host (biology) , stability (learning theory) , control theory (sociology) , equilibrium point , optimal control , mathematics , biology , mathematical optimization , control (management) , computer science , ecology , physics , immunology , helminths , mathematical analysis , medicine , population , environmental health , differential equation , artificial intelligence , telecommunications , quantum mechanics , machine learning , programming language , nonlinear system
In this paper we formulate a dynamical model to study the transmission dynamics of schistosomiasis in humans and snails. We also incorporate bovines in the model to study their impact on transmission and controlling the spread of Schistosoma japonicum in humans in China. The dynamics of the model is rigorously analyzed by using the theory of dynamical systems. The theoretical results show that the disease free equilibrium is globally asymptotically stable if R0 < 1, and if R0 > 1 the system has only one positive equilibrium. The local stability of the unique positive equilibrium is investigated and sufficient conditions are also provided for the global stability of the positive equilibrium. The optimal control theory are further applied to the model to study the corresponding optimal control problem. Both analytical and numerical results suggest that: (a) the infected bovines play an important role in the spread of schistosomiasis among humans, and killing the infected bovines will be useful to prevent transmission of schistosomiasis among humans; (b) optimal control strategy performs better than the constant controls in reducing the prevalence of the infected human and the cost for implementing optimal control is much less than that for constant controls; and