Modeling the effects of air pollutants and meteorological factors on scarlet fever in five provinces, Northwest China, 2013–2018

Abstract

As a common infectious disease, scarlet fever has exposed a tendency of slow fluctuating ups and downs in recent years with a certain periodicity. In this work, a novel differential equation epidemic model with freely transmitted viruses is introduced to investigate the transmission dynamics of scarlet fever in Northwest China. First, the correlation analysis reveals that the incidence rate of scarlet fever is significantly positively correlated with air pressure (r = 0.61), conversely negatively correlated with precipitation (r = −0.15). Furthermore, the basic reproduction number R0 is derived, and this paper proves that the unique disease-free periodic solution P0 is globally symptotically stable when R0 < 1, while the disease is uniformly persistent and at least one positive periodic solution exists when R0 > 1. Moreover, by studying the qualitative of correlation between the effective reproduction number and air pollutants or meteorological factors, the seasonal variation pattern of incidence is summarized. Our investigations suggest that the relevant epidemic prevention departments should pay close attention to changes in environmental factors of the five provinces of Northwest China to formulate timely prevention strategies before the arrival of the high-risk period.