Vector born disease account for about one third of all cases of emerging diseases. Culex sp., particularly, is one of the most important mosquito vectors transmitting important diseases such as the West Nile virus, filariasis and related encephalitis. Because there are no vaccines available the most effectual means to prevent infections from the above diseases, is to target mosquitos to prevent bites and disease transmission. However, to be effective such a strategy, it is important to predict the temporal change in mosquito abundance as well as to study how it is affected by weather conditions. This dissertation is devoted on the development of new methods to predict arthropod vector dynamics and with emphasis on the development of stochastic models and computational methods for predicting Culex sp. abundance in Northern Greece. The current dissertation is divided in three parts. The first part explores the non-trivial associations between Culex sp. mosquito abundance and weather variables using traditional and straightforward novel techniques. The information from the first part was a prerequisite for developing a series of stochastic prediction models based on the most detrimental factors affecting mosquito abundance. In the second part, a series of conventional and conditional stochastic Markov chain models are applied for the first time to predict the non-linear dynamics of Culex sp. adult abundance. In the third part of the dissertation a soft computing approach is introduced to model the population dynamics of Culex sp. and a series of autoregressive artificial neural networks are implied. Finally, the information of the models is extrapolated and a machine learning algorithm is proposed to be used for predicting arthropod vector dynamics having practical implications for public health decision making. Based on the current results there was a high and positive correlation between temperature and mosquito abundance during both observation years (r = 0.6). However, a very poor correlation was observed between rain and weekly mosquito abundances (r = 0.29), as well as between wind speed (r = 0.29), respectively. Additionally, according to the multiple linear regression model the effect of temperature, was significant. The continuous power spectrum of the mosquito abundance counts and mean temperatures depict in most cases similar power for periods which are close to 1 week, indicating the point of the lowest variance of the time series, although appearing on slightly different moments of time. The cross wavelet coherent analysis showed that inter weekly cycles with a period between 2 and 3 weeks between mosquito abundance and temperature were coherent mostly during the first and the last weeks of the season. Hence, the wavelet analysis shows a progressive oscillation in mosquito occurrences with time, which is higher at the start and the end of the season. Moreover, in contrast with standard methods of analysis, wavelets can provide useful insights into the time-resolved oscillation structure of mosquito data and accompanying revealing a non-stationary association with temperature. According to the correlation results a climate-conditioned Markov Chain (CMC) model was developed and applied for the first time to predict the dynamics of vectors of important medical diseases. Temporal changes in mosquito population profiles were generated to simulate the probabilities of a high population impact. The probabilities achieved from the trained model are very near to the observed data and the CMC model satisfactorily describes the temporal evolution of the mosquito population process. In general, our numerical results indicate that it is more likely for the population system to move into a state of high population level, when the former is a state of a low population level than the opponent. Field data on frequencies of successive mosquito population levels, which were not used for the data inferred MC modeling, were assembled to obtain an empirical intensity transition matrix and the observed frequencies. The findings match to a certain degree the empirical results in which the probabilities follow analogous patterns while no significant differences were observed between the transition matrices of the CMC model and the validation data (ChiSq=14.58013, df=24, p=0.9324451). Furter, a soft system computing modeling approach was followed to simulate and predict Culex sp. abundances. Three dynamic artificial neural network (ANNs) models were developed and applied to describe and predict the non-linear incidence and time evolution of a medical important mosquito species Culex sp. in Northern Greece. The first is a simple nonlinear autoregressive ANN model that used lagged population values as inputs, the second is an exogenous non-linear autoregressive recurrent neural network (NARX), which is designed to take as inputs the temperature as exogenous variable and mosquito abundance as endogenous. Finally, the third model is a focused time-delay neural network (FTD), which takes in to account only the temperature variable as input to provide forecasts of the mosquito abundance as target variable. All three models behaved well considering the non-linear nature of the adult mosquito abundance data. However, the NARX model, which takes in to account temperature, showed the best overall modelling performances. Nevertheless, although, the NARX model predicted slight better (R=0.623) compared to the FTD model (R=0.534), the advantage of the FTD over the NARX neural network model is that it can be applied in the case where past values of the population system, here mosquito abundance, are not available for their forecasting. This is very important considering that arthropod vector data are not always available as climatic data. Concluding, the proposed methods for simulating and predicting mosquito dynamics are recommended as viable for modeling vector disease population dynamics in order to make real-time recommendations utile for dynamic health policies decision making. The proposed stochastic models, as well as the current computational and machine learning techniques, of this work provide an accurate abstraction of the arthropod vector population progress observed within the dataset used for their generation. Nevertheless, the current study may consider also as a new entry point into the extensive literature of ecological modelling, medical entomology, as well as in simulating arthropod vector diseases epidemics. From a public health standpoint, the current models have the potential to be integrated into a decision support system allowing health policy makers in their planning to initiate specific management actions against the period of high activity of mosquito adults.