Parameter estimation of modeling schistosomiasis transmission for four provinces in China

Long-xing Qi; Yanwu Tang; Shou-jing Tian; Long-xing Qi; Yanwu Tang; Shou-jing Tian

doi:10.3934/mbe.2019047

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 2: 1005-1020. doi: 10.3934/mbe.2019047

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Parameter estimation of modeling schistosomiasis transmission for four provinces in China

1.
School of Mathematical Sciences, Anhui University, Hefei, 230601, P.R.China
2.
School of Mathematics and Computer Science, Anqing Normal University, Anqing, 246011, P.R.China

Received: 07 November 2018 Accepted: 27 December 2018 Published: 30 January 2019

According to monitoring data of Anhui, Jiangxi, Hubei, Jiangsu Provinces, in this paper the transmission of schistosomiasis is studied based on Barbour's mathematical model. The values of the basic reproduction number and key parameters are obtained with two methods. The first method is to calculate directly by using parameter values in references. The second one is to estimate parameter values by the methods of noise measurement and data smoothing and then to obtain new values of basic reproduction number. Comparing these two methods, we found the second method is good to fit the data. This parameter values can be used as reference values in other provinces. Finally, some numerical simulations are carried out to discuss the development trend of prevalence of humans and snails in each province. It is found that schistosomiasis in four provinces is expected to be eliminated with the improvement or maintenance of the standards of prevention and control. Furthermore, the time needed is di erent in the di erent four provinces.
- schistosomiasis,
- Barbour’s model,
- basic reproduction number,
- parameter estimation
Citation: Long-xing Qi, Yanwu Tang, Shou-jing Tian. Parameter estimation of modeling schistosomiasis transmission for four provinces in China[J]. Mathematical Biosciences and Engineering, 2019, 16(2): 1005-1020. doi: 10.3934/mbe.2019047

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Abstract

According to monitoring data of Anhui, Jiangxi, Hubei, Jiangsu Provinces, in this paper the transmission of schistosomiasis is studied based on Barbour's mathematical model. The values of the basic reproduction number and key parameters are obtained with two methods. The first method is to calculate directly by using parameter values in references. The second one is to estimate parameter values by the methods of noise measurement and data smoothing and then to obtain new values of basic reproduction number. Comparing these two methods, we found the second method is good to fit the data. This parameter values can be used as reference values in other provinces. Finally, some numerical simulations are carried out to discuss the development trend of prevalence of humans and snails in each province. It is found that schistosomiasis in four provinces is expected to be eliminated with the improvement or maintenance of the standards of prevention and control. Furthermore, the time needed is di erent in the di erent four provinces.

References

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