This paper focuses on the design and analysis of short-term control intervention measures seeking to suppress local populations of Aedes aegypti mosquitoes, the major transmitters of dengue and other vector-borne infections. Besides traditional measures involving the spraying of larvicides and/or insecticides, we include biological control based on the deliberate introduction of predacious species feeding on the aquatic stages of mosquitoes. From the methodological standpoint, our study relies on application of the optimal control modeling framework in combination with the cost-effectiveness analysis. This approach not only enables the design of optimal strategies for external control intervention but also allows for assessment of their performance in terms of the cost-benefit relationship. By examining numerous scenarios derived from combinations of chemical and biological control measures, we try to find out whether the presence of predacious species at the mosquito breeding sites may (partially) replace the common practices of larvicide/insecticide spraying and thus reduce their negative impact on non-target organisms. As a result, we identify two strategies exhibiting the best metrics of cost-effectiveness and provide some useful insights for their possible implementation in practical settings.

Over the last decade, the release of Wolbachia-infected Aedes aegypti into the natural habitat of this mosquito species has become the most sustainable and long-lasting technique to prevent and control vector-borne diseases, such as dengue, zika, or chikungunya. However, the limited resources to generate such mosquitoes and their effective distribution in large areas dominated by the Aedes aegypti vector represent a challenge for policymakers. Here, we introduce a mathematical framework for the spread of dengue in which competition between wild and Wolbachia-infected mosquitoes, the cross-contagion patterns between humans and vectors, the heterogeneous distribution of the human population in different areas, and the mobility flows between them are combined. Our framework allows us to identify the most effective areas for the release of Wolbachia-infected mosquitoes to achieve a large decrease in the global dengue prevalence.

This work proposes the integration of several disciplines such as mathematics, geography, and medicine. From the first one, of great importance in this project, it was possible to model the dynamics of dengue in the city of Cali, Colombia, to study its behavior; the second one, no less relevant, allowed the spatial analysis of it; and the third one, from epidemiology, allowed to know the central aspects of this disease, and its endemic and epidemic expression in the city. All of them are seen from the perspective of the Social Theory of Risk, which made it possible to recognize the integral dimension of risk, especially in coherence with public policy, of enormous relevance for subsequent management. These disciplines are integrated around the dengue epidemics in Cali, which has been living with this disease for several decades and has not been able to eradicate it or at least prevent epidemic outbreaks in its population. This work intends to propose controls to mitigate dengue epidemics in the city by considering social variables, such as the mobility of people, and epidemiological variables, such as the spatial-temporal behavior of the disease. It is hoped that this work will lay some foundations that support and link the relationship between environmental health and risk management, since both aim to generate safe environments that contribute to the welfare of communities.

Diaphorina citri is the primary vector of Huanglongbing (HLB), a devastat- ing disease that affects global citrus production. Effective biological control using the parasitoid Tamarixia radiata represents a sustainable alternative to chemical insecticides, but its efficacy depends heavily on environmental variables and resource availability. In this work, we develop a four-population mathematical model to analyze the dynamics of D. citri in the presence of T. radiata, a known parasitoid. Our model incorporates the cyclical and pe- riodic behavior of citrus flushing (new shoots), providing a realistic represen- tation of resource-limited dynamics as observed in field conditions. Through comparative simulations of three scenarios, without parasitoid, a single ini- tial introduction, and periodic augmentative releases, we characterize and compare the impact of T. radiata as a biological control agent. Our results show that periodic releases maintain pest suppression, whereas a single introduction only delays pest recovery. By aligning theoretical modeling with ecological reality, this framework supports the role of T. radiata in pest sup- pression and provides a baseline for future work on optimal and cost-effective release strategies.

En este trabajo plantea un modelo para la dinámica de la tuberculosis, el cual considera la población latente de bajo riesgo con el objetivo de evaluar la importancia de incluirla en el modelo y determinar si es necesario tratarla y/o controlarla. Para ello, se realizó un análisis cualitativo, determinando qué parámetros tienen mayor relevancia en la transmisión inicial de la enfermedad y calculando cuál es el número promedio de nuevas infecciones producidas por un individuo infeccioso. Se formuló y resolvió numéricamente un problema de control óptimo, en el cual se busca minimizar tanto los infectados como los costos económicos que estos impliquen la implementación de los controles en la dinámica de la tuberculosis planteada. Se utilizaron simulaciones numéricas para analizar los efectos de implementar los controles obtenidos. Por último, se realizaron simulaciones para Cali (Colombia), estableciendo una metodología para el diseño de estrategias de control para reducir la transmisión de la tuberculosis en la ciudad. This work proposes a model for the dynamics of tuberculosis, which considers a latent low-risk population, with the aim of evaluating the importance of including it in the model and determining whether it is necessary to treat and/or control it. To this effect, a qualitative analysis of the model was carried out, determining which parameters are most relevant in the initial transmission of the disease and calculating the average number of new infections produced by an infectious individual. An optimal control problem was formulated and numerically solved, which seeks to minimize both the infected and the economic costs generated by the implementation of controls in the proposed dynamics of tuberculosis. Numerical simulations were used to analyze the effects of implementing the controls obtained. Finally, simulations are carried out for Cali (Colombia), establishing a methodology for the design of control strategies aimed at reducing the transmission of tuberculosis in the city.