The impact of temperature, humidity and closing school on the mumps epidemic: a case study in the mainland of China

Abstract

Background: To control resurging infectious diseases like mumps, it is necessary to resort to effective control and preventive measures. These measures include increasing vaccine coverage, providing the community with advice on how to reduce exposure, and closing schools. To justify such intervention, it is important to understand how well each of these measures helps to limit transmission.

Methods: In this paper, we propose a simple SEILR (susceptible-exposed-symptomatically infectious-asymptomatically infectious-recovered) model by using a novel transmission rate function to incorporate temperature, humidity, and closing school factors. This new transmission rate function allows us to verify the impact of each factor either separately or combined. Using reported mumps cases from 2004 to 2018 in the mainland of China, we perform data fitting and parameter estimation to evaluate the basic reproduction number $R_0$ . As a wide range of one-dose measles, mumps, and rubella (MMR) vaccine programs in China started only in 2008, we use different vaccination proportions for the first Stage I period (from 2004 to 2008) and the second Stage II period (from 2009 to 2018). This allows us to verify the importance of higher vaccine coverage with a possible second dose of MMR vaccine.

Results: We find that the basic reproduction number $R_0$ is generally between 1 and 3. We then use the Akaike Information Criteria to assess the extent to which each of the three factors contributed to the spread of mumps. The findings suggest that the impact of all three factors is substantial, with temperature having the most significant impact, followed by school opening and closing, and finally humidity.

Conclusion: We conclude that the strategy of increasing vaccine coverage, changing micro-climate (temperature and humidity), and closing schools can greatly reduce mumps transmission.

Keywords: Basic reproduction number; Data fitting; Humidity; Mumps; School opening and closing; Temperature.

Fig. 1

Three temperature zones of the mainland of China. ((I) Subtropical: Hainan, Guangdong, Guangxi, Yunnan, Jiangxi, Hunan, Chongqing, Guizhou, Fujian, Zhejiang, Hubei, Jiangsu, Sichuan, Anhui, Shanghai (Hainan is actually tropical, but because there is only one Hainan in the tropics, Hainan is classified as subtropical here for the convenience of discussion); (II) Temperate: Shandong, Beijing, Tianjin, Shanxi, Hebei, Henan, Shaanxi, Gansu, Xinjiang, Ningxia, Jilin, Heilongjiang, Liaoning, and Inner Mongolia; (III) The vertical temperature zone: Tibet and Qinghai.)

Fig. 2

Flowchart of mumps transmission in a population

Fig. 3

Temperature function $f_1\left(t\right)$, the relative humidity function $f_2\left(t\right)$, the school opening and closing function $f_3\left(t\right)$, and the transmission rate function $\beta \left(t\right)$ in the model $U_1$

Fig. 4

The fitting effects of four models ($U_1$-$U_4$)

Fig. 5

Show the PRCC of parameters with ${\Re }_0$

Fig. 6

PRCC of parameters in continuous time

Fig. 7

The value of ${\Re }_0$ for each province in the mainland of China