Narrow Results

This study introduces a mathematical model aimed at evaluating the potential influence of aerosol introduction into the atmosphere for inducing rainfall and managing atmospheric pollution. By expanding on the proposed model, we incorporate stochastic elements to encompass environmental white noises that impact the system’s dynamics. Both mathematical and numerical methods are employed to analyze the system’s behavior. In the context of the deterministic model, we examine the solutions’ positivity and boundedness, identify feasible equilibria, and scrutinize the stability characteristics both locally and globally. The analysis of the stochastic system encompasses discussions regarding the existence of a unique solution, its ultimate boundedness, and the conditions that prompt the establishment of a unique stationary distribution characterized by ergodic properties. Our simulations illustrate that augmenting cloud formation rates and externally introduced aerosols can amplify rainfall while mitigating atmospheric pollution levels. Minor intensities of white noise do not alter the system’s behavior, whereas significant intensities result in high-amplitude oscillations of the system’s variables. We explore the effects of white noise intensities using histograms and stationary distributions, highlighting long-term rainfall trends in a noisy environment.

This paper introduces a new technique in ecology to analyze spatial and temporal variability in environmental variables. By using simple statistics, we explore the relations between abiotic and biotic variables that influence animal distributions. However, spatial and temporal variability in rainfall, a key variable in ecological studies, can cause difficulties to any basic model including time evolution.

The study was of a landscape scale (three million square kilometers in eastern Australia), mainly over the period of 1998–2004. We simultaneously considered qualitative spatial (soil and habitat types) and quantitative temporal (rainfall) variables in a Geographical Information System environment. In addition to some techniques commonly used in ecology, we applied a new method, Functional Principal Component Analysis, which proved to be very suitable for this case, as it explained more than 97% of the total variance of the rainfall data, providing us with substitute variables that are easier to manage and are even able to explain rainfall patterns. The main variable came from a habitat classification that showed strong correlations with rainfall values and soil types.

The sterile insect technique (SIT) is a biological control technique that can be used either to eliminate or decay a wild mosquito population under a given threshold to reduce the nuisance or the epidemiological risk. In this work, we propose a model using a differential system that takes into account the variations of rainfall and temperature over time and study their impacts on sterile males’ releases strategies. Our model is as simple as possible to avoid complexity while being able to capture the temporal variations of an Aedes albopictus mosquito population in a domain treated by SIT, located in Réunion island. The main objective is to determine what period of the year is the most suitable to start a SIT control to minimize the duration of massive releases and the number of sterile males to release, either to reduce the mosquito nuisance, or to reduce the epidemiological risk. Since sterilization is not $100\%$ efficient, we also study the impact of different levels of residual fertility within the released sterile males population. Our study shows that rainfall plays a major role in the dynamics of the mosquito and the SIT control, that the best period to start a massive SIT treatment lasts from July to December, that residual fertility has to be as small as possible, at least for nuisance reduction. Indeed, when the main objective is to reduce the epidemiological risk, we show that residual fertility is not necessarily an issue. Increasing the size of the releases is not always interesting. We also highlight the importance of combining SIT with mechanical control, i.e., the removal of breeding sites, in particular when the initial mosquito population is large. Last but not least our study shows the usefulness of the modeling approach to derive various simulations to anticipate issues and demand in terms of sterile insects’ production.

As the source of replenishment, rainfall has an extensive impact because its variability shapes biologically efficient pulses of soil moisture recharge across layers from rainfall events. In this paper, a mathematical model is proposed to explore the importance of transpiration from agricultural crops and aerosols on the pattern of rainfall. For the system without seeding, the simulation results show destabilizing roles of parameters related to formation of cloud drops due to transpiration of agricultural crops, formation of raindrops due to cloud drops and growth of agricultural crops due to rain. The model without seeding is extended to its stochastic counterpart to encapsulate the uncertainty observed in some important parameters. We observe the variability in the system’s variables and found their distributions at certain fixed times, which explore the importance of stochasticity in the system. Our findings show that transpiration through agricultural crops plays an important role in cloud formation, and thus, affects the effectiveness of different rainfall events. Moreover, the combined actions of transpiration and seeding are much more beneficial in producing rain. Finally, we see the behavior of system by considering seasonal variations of some rate parameters.