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Human trafficking is a heartless crime that represents the second most profitable crime in the world. Mexico's geographical position makes it a country with high levels of human trafficking. Using the snowball sampling method, the major contribution of this paper is the abstraction of the human trafficking network on the southern border of Mexico. Based on a social network analysis, it is identified that the criminal network is moderately centralized (44.32%) and with medium density (0.401). Therefore, the network has minimal cohesiveness and members may find it difficult to share information, money, or products among themselves. To evaluate different dismantling strategies to tackle the criminal organization, three algorithms are evaluated. We found that the first actors to be removed are neither the most connected nor the most peripheral, but the actors who are moderately connected to people of their kind should be removed. In summary, this paper provides a significant step forward to understand quantitatively human trafficking networks and evaluate the limits of dismantling strategies.

Several mathematical models in SARS-CoV-2 have shown how target-cell model can help to understand the spread of the virus in the host and how potential candidates of antiviral treatments can help to control the virus. Concepts as equilibrium and stability show to be crucial to qualitatively determine the best alternatives to schedule drugs, according to effectivity in inhibiting the virus infection and replication rates. Important biological events such as rebounds of the infections (when antivirals are incorrectly interrupted) can also be explained by means of a dynamic study of the target-cell model. In this work, a full characterization of the dynamical behavior of the target-cell models under control actions is made and, based on this characterization, the optimal fixed-dose antiviral schedule that produces the smallest amount of dead cells (without viral load rebounds) is computed. Several simulation results - performed by considering real patient data - show the potential benefits of both, the model characterization and the control strategy.

Mathematical models describing SARS-CoV-2 dynamics and the corresponding immune responses in patients with COVID-19 can be critical to evaluate possible clinical outcomes of antiviral treatments. In this work, based on the concept of virus spreadability in the host, antiviral effectiveness thresholds are determined to establish whether or not a treatment will be able to clear the infection. In addition, the virus dynamic in the host -- including the time-to-peak and the final monotonically decreasing behavior -- is chracterized as a function of the treatment initial time. Simulation results, based on nine real patient data, show the potential clinical benefits of a treatment classification according to patient critical parameters. This study is aimed at paving the way for the different antivirals being developed to tackle SARS-CoV-2.

While many epidemiological models have being proposed to understand and handle COVID-19, too little has been invested to understand how the virus replicates in the human body and potential antiviral can be used to control the replication cycle. In this work, using a control theoretical approach, validated mathematical models of SARS-CoV-2 in humans are properly characterized. A complete analysis of the main dynamic characteristic is developed based on the reproduction number. The equilibrium regions of the system are fully characterized, and the stability of such a regions, formally established. Mathematical analysis highlights critical conditions to decrease monotonically SARS-CoV-2 in the host, such conditions are relevant to tailor future antiviral treatments. Simulation results show the potential benefits of the aforementioned system characterization.

The precise mechanism that causes HIV infection to progress to AIDS is still unknown. This paper presents a mathematical model which is able to predict the entire trajectory of the HIV/AIDS dynamics, then a possible explanation for this progression is examined. A dynamical analysis of this model reveals a set of parameters which may produce two real equilibria in the model. One equilibrium is stable and represents those individuals who have been living with HIV for at least 7 to 9 years, and do not develop AIDS. The other one is unstable and represents those patients who developed AIDS in an average period of 10 years. However, further work is needed since the proposed model is sensitive to parameter variations., Comment: Accepted in proceedings of 18th IFAC World Congress, Milan, August 28 - September 2, 2011 (Invited Contribution: Modeling methods and clinical applications in medical and biological systems I). 6 pages, 7 figures