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A schistosomiasis compartment model with incubation and its optimal control
Author(s) -
Ding Chunxiao,
Sun Yun,
Zhu Yuanguo
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4372
Subject(s) - schistosomiasis , mathematics , basic reproduction number , compartment (ship) , stability (learning theory) , incubation period , incubation , equilibrium point , control (management) , optimal control , mathematical optimization , control theory (sociology) , mathematical economics , computer science , biology , mathematical analysis , differential equation , immunology , medicine , artificial intelligence , helminths , environmental health , biochemistry , oceanography , geology , population , machine learning
A new mathematical model included an exposed compartment is established in consideration of incubation period of schistosoma in human body. The basic reproduction number is calculated to illustrate the threshold of disease outbreak. The existence of the disease free equilibrium and the endemic equilibrium are proved. Studies about stability behaviors of the model are exploited. Moreover, control measure assessments are investigated in order to seek out effective control interventions for anti‐schistosomiasis. Then, the corresponding optimal control problem according to the model is presented and solved. Theoretical analyses and numerical simulations induce several prevention and control strategies for anti‐schistosomiasis. At last, a discussion is provided about our results and further work. Copyright © 2017 John Wiley & Sons, Ltd.