Dengue is one of the most rapidly spreading vector-borne diseases, which is considered to be a major health concern in tropical and sub-tropical countries. It is strongly believed that the spread and abundance of vectors are related to climate. Construction of climate-based mathematical model that integrates meteorological factors into disease infection model becomes compelling challenge since the climate is positively associated with both incidence and vector existence. A host-vector model is constructed to simulate the dynamic of transmission. The infection rate parameter is replaced with the time-dependent coefficient obtained by optimization to approximate the daily dengue data. Further, the optimized infection rate is denoted as a function of climate variables using the Autoregressive Distributed Lag (ARDL) model. The infection parameter can be extended when updated daily climates are known, and it can be useful to forecast dengue incidence. This approach provides proper prediction, even when tested in increasing or decreasing prediction windows. In addition, associations between climate and dengue are presented as a reversed slide-shaped curve for dengue-humidity and a reversed U-shaped curves for dengue-temperature and dengue-precipitation. The range of optimal temperature for infection is 24.3–30.5 °C. Humidity and precipitation are positively associated with dengue upper the threshold 70% at lag 38 days and below 50 mm at lag 50 days, respectively. Identification of association between climate and dengue is potentially useful to counter the high risk of dengue and strengthen the public health system and reduce the increase of the dengue burden.

Background: The popularity of dengue can be inferred from Google Trends that summarizes Google searches of related topics. Both the disease and its Google Trends have a similar source of causation in the dengue virus, leading us to hypothesize that dengue incidence and Google Trends results have a long-run equilibrium. Objective: This research aimed to investigate the properties of this long-run equilibrium in the hope of using the information derived from Google Trends for the early detection of upcoming dengue outbreaks. Methods: This research used the cointegration method to assess a long-run equilibrium between dengue incidence and Google Trends results. The long-run equilibrium was characterized by their linear combination that generated a stationary process. The Dickey-Fuller test was adopted to check the stationarity of the processes. An error correction model (ECM) was then adopted to measure deviations from the long-run equilibrium to examine the short-term and long-term effects. The resulting models were used to determine the Granger causality between the two processes. Additional information about the two processes was obtained by examining the impulse response function and variance decomposition. Results: The Dickey-Fuller test supported an implicit null hypothesis that the dengue incidence and Google Trends results are nonstationary processes (P=.01). A further test showed that the processes were cointegrated (P=.01), indicating that their particular linear combination is a stationary process. These results permitted us to construct ECMs. The model showed the direction of causality of the two processes, indicating that Google Trends results will Granger-cause dengue incidence (not in the reverse order). Conclusions: Various hypothesis testing results in this research concluded that Google Trends results can be used as an initial indicator of upcoming dengue outbreaks.

Measles is a contagious disease caused by the measles virus of genus Morbillivirus, which has been spreading in many affected regions. This infection is characterized by the appearance of rashes all over the body and potentially cause serious complications, especially among infants and children. Before measles immunization was promoted, it is one of the endemic diseases that caused the most fatalities each year in the world. This paper aims to analyze and to investigate measles transmission in Jakarta via an SIHR epidemic model involving vaccination from January to December 2017. Jakarta Health Office collected the observed data of measles incidence. We then derived the basic reproduction number as a threshold of disease transmission and obtained the local as well as global stability of the equilibria under certain conditions. The unobserved parameters and initial conditions were estimated by minimizing errors between data and numerical results. Furthermore, a stochastic model was developed to capture the data and to accommodate the randomness of the transmission. Sensitivity analysis was also performed to analyze and to identify the parameters which give significant contributions to the spread of the virus. We then obtained simulations of vaccine level coverage. The data is shown within a 95% confidence interval of the stochastic solutions, and the average of the stochastic solutions is relatively close to the solution of the deterministic model. The most sensitive parameter in the infected compartment is the hospitalized rate, which can be considered to be one of the essential factors to reduce the number of cases for policymakers. We hence proposed a control strategy which is providing treatment accesses easier for infected individuals is better than vaccinating when an outbreak occurs.

Dengue is a potentially lethal mosquito-borne disease, regarded as the most dangerous disease in the world. It is also a major health issue in tropical and subtropical countries. Environmental characteristics and sociocultural are factors which play a role in the spread of dengue. Different landscape structure such as lowland and highland areas are possible to give different infection rate on dengue transmission. Semarang and Malang are densely populated areas in Java, which are selected to be our study areas. A mathematical model (SIR-UV) is adapted to describe dengue transmission. Spiral dynamic optimization is applied to convert monthly data to weekly in Malang and estimate the infection rate that minimized the deviation between dengue data and simulation. This method produces a good fitting to the data. We compare the pattern of dengue cases from the simulation in both cities. Furthermore, we identify seasonal variations of the cases via Fourier series of the infection rate. We also investigate the correlation between humidity, infection rate, and dengue cases in Semarang and Malang. It reveals that humidity influences infection rate in 1-3 weeks later and the infection rate produces dengue cases in the next four weeks.