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We establish a compartmental model to study the transmission of Zika virus disease including spread through sexual contacts and the role of asymptomatic carriers. To incorporate the impact of the seasonality of weather on the spread of Zika, we apply a nonautonomous model with time-dependent mosquito birth rate and biting rate, which allows us to explain the differing outcome of the epidemic in different countries of South America: using Latin Hypercube Sampling for fitting, we were able to reproduce the different outcomes of the disease in various countries. Sensitivity analysis shows that, although the most important factors in Zika transmission are the birth rate of mosquitoes and the transmission rate from mosquitoes to humans, spread through sexual contacts also highly contributes to the transmission of Zika virus: our study suggests that the practice of safe sex among those who have possibly contracted the disease, can significantly reduce the number of Zika cases.

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To overcome well-known difficulties in establishing reliable models based on large data sets, the Random Forest Regression (RFR) method is applied to study economical breeding and milk production of dairy cows. As for the features of RFR, there are several positive experiences in various areas of applications supporting that with RFR one can achieve reliable model predictions for industrial production of any product providing a useful base for decisions. In this study, a data set of a period of ten years including about eighty thousand cows was analysed by means of RFR. Ranking of production control parameters is obtained, the most important explanatory variables are found by computing the variances of the target variable on the sets created during the training phases of the RFR. Predictions are made for the milk production and the conception of the calves with high accuracy on given data and simulations are used to investigate prediction accuracy. This paper is primarily concerned with the mathematical aspects of a forthcoming work focused on the agricultural viewpoints. As for future mathematical research plans, the results will be compared with models based on factor analysis and linear regression.