Weather and environmental factors affect dengue transmission patterns through the interactive dynamics between mosquito ecology and vector–human transmission. Due to dengue fever is prevalent in southern Taiwan, and government agencies were frequently using of anti-mosquito drugs for epidemic prevention which not only costs high but also increases the evolutionary pressure of vector mosquitoes, forcing young mosquitoes or larva to develop resistance and improve their survival ability. The solution for infectious disease prevention and control is the identification of the best intervention timing to disrupt the growth cycle by applying insecticides at the right phase of disease diffusion. In such a way, the cost of control can be effective, and epidemic incidents can be controlled before sensible damages occur. This study aims to develop a forecasting method for intelligent epidemic prevention.
The growth process of arthropod-borne infectious diseases should be understood to formulate effective epidemic prevention strategies. A diffusion model of the differential equation commonly used in mathematical epidemiology is adopted in this study to predict the transmission pattern of dengue fever in the next few years based on the recorded dengue fever data in Kaohsiung from 2006 to 2016 [1, 2]. In the 10-year data from the Health Bureau of Kaohsiung Municipal Government, 896 zones of Kaohsiung are included in several years. However, few cases are reported in only 251 zones, and only district data are available in most of the years. The number of reported cases is not equivalent to the number of infected patients. In this study, this issue is addressed using a negative binomial distribution. The data obtained include not only the number of cases but also the area, population, temperature, humidity, rainfall, the population of schools, and Breteau index of adult mosquitoes in each locality. Qianzhen District, with the most dengue cases, is selected as an example. Although temperature variations in these several years are similar, the number of people infected per thousand was lower in 2014 with a high mosquito index than that in the next year with a higher mosquito index.
Regardless of the trend in diffusion time-sequence change, the year with the most dengue fever cases is used to conduct static spatial thermal zone analysis. Hausdorff distance verification shows that the area where dengue fever appears with the highest probability includes most areas in Qianzhen District, and the area with the second-highest possibility is No. 3 resident region. Spatial verification result is similar to general cognition. Therefore, the basis of this study is appropriate. On the basis of the spatial analysis result, we estimate and calibrate the diffusion model of dengue fever infection in the densest areas and the population of Kaohsiung as a whole to predict the trend of dengue fever occurred in the coming year.
The issue of intelligent epidemic prevention is extremely challenging. Assuming that only one short time of mosquito eradication can be conducted for an infinite generation of mosquitoes, we find that if mosquito eradication is carried out at the early stage of the host’s onset, the mosquitoes produced later still bite an infectious host. Since then, a mosquito vector has remained infectious for generations. However, if the timing of mosquito eradication is too late, the host population is infected. As such, epidemic prevention fails. Theoretically, if hosts are fully infected and healed, the best time point should be at the time when hosts are just healed. Therefore, the choice of this time point depends on the prevalence of hosts but not on the growth conditions of mosquitoes. The use of environmental temperature to regress the prevalence of infectious diseases is inappropriate. Infected hosts and vectors are dynamically diffusive in time and asymmetrically mobile in space. The best time point must be known through special analytical methods and lengthy and complicated operations.
Studies have been widely performed on general epidemic prevention and surveillance, as well as epidemic control, but such studies remain incomplete. Shen et al.  analyzed the data of a small number of clinical case reports by using the Bayes probability algorithm and proposed a time prediction model for future outbreaks of infectious diseases throughout the city. Difficulties in dengue fever epidemic prevention include the poorly described trend and dynamics of vector mosquitoes. Therefore, no complete solution has been proposed.
Andraud et al.  reviewed 42 dynamic models of dengue fever transmission in the time dimension and completely classified them to describe the dynamic transmission models of these vector-borne infections and their corresponding control methods. Nuraini et al.  discussed the transmission dynamics of dengue hemorrhagic fever caused by the cross-infection of different dengue viruses and proposed a control method to eliminate the stable balance by equilibrium solutions of two or more serotype infections.
Nishiura et al.  estimated the basic transmission value R0 and found that dengue fever is a periodic epidemic disease. This periodicity affects the transmission ability of mosquito vectors or R0 but does not influence environmental factors. R0 is also a variable related to specific environmental factors so that it can predict prevalence in the coming year. Therefore, the regression model analysis is inappropriate without considering the transmission capacity of mosquito vectors. Amaku et al.  and Polwiang  compared two kinds of vector-borne infectious models and emphasized the advantages and disadvantages of both models as the foundation of future model improvements.
Zamiri et al.  investigated the epidemic outbreaks in temporal and spatial patterns by an SIR nonlinear dynamic model without considering the influence of vectors. Similar to our study, they also suggest that numerical studies can help the early prediction of the epidemic in terms of peak and duration. Chang et al.  re-emphasized the importance of understanding the transmission dynamics and suggested the prediction of dengue epidemic can be an early warning tool. Kilicman  contended that dengue transmission possesses memory by analyzing the SIR epidemic model. Cahyono et al.  analyzed the range of parameters that lead to the stability of the dengue fever SIR model. Although the epidemic research of dengue fever applies the SIR model extensively, however, few studies can estimate parameters from the case records of real clinic reports. The insufficiency is partly due to the computational difficulty. Our study thus overcame the difficulty and obtained the parameters through an advanced Bayesian technique.
Finally, few studies have assessed dengue epidemic control. Gersovitz and Hammer  analyzed the economic effects of investment on epidemic prevention and assessed the cost-effectiveness of policies. Chanprasopchai et al.  investigated the effect of dengue vaccination through the SIR model, leaving aside the safety dispute, and suggested a significant reduction of hospitalization time. In Rio de Janeiro, 43 different insecticidal strategies were applied to adult mosquitoes and larvae for 5 years. Studies on the insecticide resistance of vector mosquitoes have shown that frequent insecticide applications are costly and may lead to the development of insecticide resistance in larvae .