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Background  Malaria is one of the most severe parasitic diseases in the world. Spatial distribution estimation of malaria and its future scenarios are important issues for malaria control and elimination. Furthermore, sophisticated nonlinear relationships for prediction between malaria incidence and potential variables have not been well constructed in previous research. This study aims to estimate these nonlinear relationships and predict future malaria scenarios in northern China.    Methods  Nonlinear relationships between malaria incidence and predictor variables were constructed using a genetic programming (GP) method, to predict the spatial distributions of malaria under climate change scenarios. For this, the examples of monthly average malaria incidence were used in each county of northern China from 2004 to 2010. Among the five variables at county level, precipitation rate and temperature are used for projections, while elevation, water density index, and gross domestic product are held at their present-day values.    Results  Average malaria incidence was 0.107 ‰ per annum in northern China, with incidence characteristics in significant spatial clustering. A GP-based model fit the relationships with average relative error (ARE) = 8.127 % for training data (R 2  = 0.825) and 17.102 % for test data (R 2  = 0.532). The fitness of GP results are significantly improved compared with those by generalized additive models (GAM) and linear regressions. With the future precipitation rate and temperature conditions in Special Report on Emission Scenarios (SRES) family B1, A1B and A2 scenarios, spatial distributions and changes in malaria incidences in 2020, 2030, 2040 and 2050 were predicted and mapped.    Conclusions  The GP method increases the precision of predicting the spatial distribution of malaria incidence. With the assumption of varied precipitation rate and temperature, and other variables controlled, the relationships between incidence and the varied variables appear sophisticated nonlinearity and spatially differentiation. Using the future fluctuated precipitation and the increased temperature, median malaria incidence in 2020, 2030, 2040 and 2050 would significantly increase that it might increase 19 to 29 % in 2020, but currently China is in the malaria elimination phase, indicating that the effective strategies and actions had been taken. While the mean incidences will not increase even reduce due to the incidence reduction in high-risk regions but the simultaneous expansion of the high-risk areas.

Spatial distribution estimation of malaria in northern China and its scenarios in 2020, 2030, 2040 and 2050