A Temperature Conditioned Markov Chain Model for Predicting the Dynamics of Mosquito Vectors of Disease

SIMPLE SUMMARY: Understanding and predicting vector population and related disease dynamics, is crucial for gaining insight into the abundance and dynamics of arthropod disease vectors, and for the design of effective vector control strategies. Several mathematical and standard epidemiological models have been proposed in studying vector transmitted infectious disease dynamics. However, most models are of deterministic nature and are not able to estimate other relevant metrics such as the probability of vector population emergence as well as the probability and expected time to reach certain population and/or infection state. Here we are focusing on stochastic modeling of mosquito abundance data using weather driven Markov chains (MCs) and are particularly interested in estimating transition probabilities (TPs) between different population levels. A MC model is based on the assumption that the future state of the variable is only dependent on the present state and is suitable in cases of short and noisy data characterized by a complex and random behavior. The aim is to introduce and generalize a formulation of conditional Markov chain models (CMSs) for predicting probability transition estimates of arthropod vector populations. In this context, first we present the basic principles and assumptions behind Markov chain modeling approach, with an intuitive interpretation of the integration of conditional Markov chains (CMCs) and then demonstrate the usefulness of the approach in predicting the abundance of Culex sp. We conclude that the conditional Markov chain technique is recommended as viable for modeling populations that explicit random dynamics and predict their future evolution. Although, the Markov models generated in this work provide an accurate abstraction of the vector disease progress observed within the dataset used for their generation, we envision the current approach as an entry point into the medical entomology literature and methods for predicting arthropod vector diseases dynamics. ABSTRACT: Understanding and predicting mosquito population dynamics is crucial for gaining insight into the abundance of arthropod disease vectors and for the design of effective vector control strategies. In this work, 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 simulated transition probabilities of the mosquito populations achieved from the trained model are very near to the observed data transitions that have been used to parameterize and validate the model. Thus, the CMC model satisfactorily describes the temporal evolution of the mosquito population process. In general, our numerical results, when temperature is considered as the driver of change, 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 lower population level than the opposite. 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 frequencies observed. Our 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). The proposed modeling approach is a valuable eco-epidemiological study. Moreover, compared to traditional Markov chains, the benefit of the current CMC model is that it takes into account the stochastic conditional properties of ecological-related climate variables. The current modeling approach could save costs and time in establishing vector eradication programs and mosquito surveillance programs.