A stage structured mosquito model incorporating effects of precipitation and daily temperature fluctuations

Highlights

• Data on Breteau index, temperature and precipitation were used for model fitting.

• The abundance of mosquitoes depends on the distribution of the precipitation.

• Large diurnal temperature differences can reduce the abundance of mosquitoes.

• Effects of increasing precipitation and temperature depend on each other.

• It is better to clear water early and spray insecticide between April and August.

Abstract

An outbreak of dengue fever in Guangdong province in 2014 was the most serious outbreak ever recorded in China. Given the known positive correlation between the abundance of mosquitoes and the number of dengue fever cases, a stage structured mosquito model was developed to investigate the cause of the large abundance of mosquitoes in 2014 and its implications for outbreaks of the disease. Data on the Breteau index (number of containers positive for larvae per 100 premises investigated), temperature and precipitation were used for model fitting. The egg laying rate, the development rate and the mortality rates of immatures and adults were obtained from the estimated parameters. Moreover, effects of daily fluctuations of temperature on these parameters were obtained and the effects of temperature and precipitation were analyzed by simulations. Our results indicated that the abundance of mosquitoes depended not only on the total annual precipitation but also on the distribution of the precipitation. The daily mean temperature had a nonlinear relationship with the abundance of mosquitoes, and large diurnal temperature differences can reduce the abundance of mosquitoes. In addition, effects of increasing precipitation and temperature were interdependent. Our findings suggest that the large abundance of mosquitoes in 2014 was mainly caused by the distribution of the precipitation. In the perspective of mosquito control, our results reveal that it is better to clear water early and spray insecticide between April and August in case of limited resources.

Introduction

In April 2015, a widespread outbreak of Zika virus disease began in Brazil and has spread to many other countries in South America, Central America, the Caribbean and Mexico. In Brazil, by the end of 2015, the Brazilian Ministry of Health estimated that 500,000–1.5 million people have been infected by the Zika virus (Paploski et al., 2016), which is a mosquito-borne virus transmitted by Aedes aegypti and A. albopictus, which also transmit other vector-borne diseases such as dengue fever and yellow fever, while species of Anopheles are the principal vectors of malaria and Culex species transmit West Nile virus and other infections. According to reports of the World Health Organization (WHO), more than 2.5 billion people in over 100 countries, approximately one-third of the world's population, are at risk of contracting dengue alone and malaria causes more than 438,000 deaths every year globally, according to the 2015World Malaria Report (http://www.who.int/malaria/publications/worldmalaria-report-2015/en/).

As a main mosquito-borne disease, dengue fever can cause a severe flu-like illness and sometimes causes a potentially lethal complication. It was first recognized in the 1950s in the Philippines and Thailand and now up to 50–100 million infections are estimated to occur annually in over 100 endemic countries. In China, epidemics of dengue fever were first reported before 1940 (Qiu et al., 1993). In 1978, a sudden outbreak of dengue fever occurred in Foshan city of Guangdong Province (Qiu et al., 1993) and it spread to seven adjacent counties and cities where a total of 22,122 cases, including 16 fatalities, were reported (Guan et al., 2000). Since then outbreaks of dengue fever have occurred frequently in southern China. The outbreak of dengue fever in Guangdong province in 2014 has been the most serious outbreak in China so far.

Mosquito-borne diseases are sensitive to climatic factors. Several studies have been carried out on the correlation between mosquito-borne diseases and climate using statistical methods and they showed significant associations between climatic variables and disease incidence (Nagao et al., 2003, Depradine and Lovell, 2004, Hsieh and Chen, 2009, Do et al., 2014). Wu et al. found a negative association of dengue incidence with temperature and relative humidity by using autoregressive models (Wu et al., 2007). Eastin et al. (2014) revealed that dengue cases increase a few weeks after the daily temperature range remains within the temperature range optimal for mosquito survival and transmission of the disease. In a study of an epidemic in Guangzhou, China, correlation analysis and time series analysis of climate data and dengue fever cases showed a positive correlation between dengue incidence and minimum and maximum temperatures, precipitation and humidities, and seasonal fluctuations in immature densities of Aedes albopictus, which were consistent with the dengue seasonality (Lu et al., 2009, Luo et al., 2012). These results indicate that climatic factors have a complex relationship with mosquito-borne disease transmission and so research on the effects of climate factors on the abundance of mosquitoes and on the transmission of mosquito-borne diseases is important.

Other studies have focused on mathematical models to investigate the epidemiology of mosquito-borne diseases by incorporating climatic factors into models. Some of these mathematical models are stage structured mosquito models considering the population dynamics of mosquitoes and climatic factors are incorporated into the reproduction, development and survival rates (Erickson et al., 2010, Beck-Johnson et al., 2013, Jia et al., 2016). For example, (Gong et al., 2011) established a climate-based model for West Nile Culex mosquito vectors in 2011. The model was validated with field data and the simulated abundance was highly correlated with actual mosquito numbers. Other mathematical models of disease dynamics are Susceptible-Exposed-Infectious-Recovered (SEIR) models, with or without considering vectors (Feng and Velasco-Hernandez, 1997, Esteva and Matias, 2001, Derouich and Boutayeb, 2006). Most of these models focus on the basic reproduction number, examine force of infection or transmission dynamics (Marques et al., 1990, Favier et al., 2006, Chowell et al., 2007, Wearing and Rohani, 2006) and climatic factors are incorporated into the transmission parameters or with a statistical model. These papers usually focus on the sensitivity of the dynamics of mosquito populations or disease transmission to climatic factors, and on seasonal trends of the abundance of mosquitoes or disease outbreaks (Nago and Koelle, 2007, Thammapalo et al., 2008, Li et al., 1985, Sanchez et al., 2006). Effects of the within- and between year spatio-temporal distributions of temperature and precipitation are rarely discussed. Besides, the effect of temperature is usually investigated under constant temperature conditions, namely the daily mean temperature. However, daily temperature fluctuations have shown to be important biologically (Carrington et al., 2013) and some studies have been published to investigate effects of daily fluctuations of temperature on the transmission parameters (Lambrechts et al., 2011, Liu-Helmersson et al., 2014). Therefore, in this paper, we mainly pay attention to a mosquito population model in relation to temperature and precipitation, which incorporates daily fluctuations of temperature. Based on previous research results and the dengue fever situation in Guangzhou in 2014, the objectives of this study were to improve knowledge of the relationships between climate and mosquito abundance, to explain the climatic reasons for the substantial outbreak of dengue fever in 2014 and to predict the effectiveness of potential control measures.