On the computational modeling of the innate immune system.

In recent years, there has been an increasing interest in the mathematical and computational modeling of the human immune system (HIS). Computational models of HIS dynamics may contribute to a better understanding of the relationship between complex phenomena and immune response; in addition, computational models will support the development of new drugs and therapies for different diseases. However, modeling the HIS is an extremely difficult task that demands a huge amount of work to be performed by multidisciplinary teams. In this study, our objective is to model the spatio-temporal dynamics of representative cells and molecules of the HIS during an immune response after the injection of lipopolysaccharide (LPS) into a section of tissue. LPS constitutes the cellular wall of Gram-negative bacteria, and it is a highly immunogenic molecule, which means that it has a remarkable capacity to elicit strong immune responses. We present a descriptive, mechanistic and deterministic model that is based on partial differential equations (PDE). Therefore, this model enables the understanding of how the different complex phenomena interact with structures and elements during an immune response. In addition, the model's parameters reflect physiological features of the system, which makes the model appropriate for general use.

Timing the race of vaccination, new variants, and relaxing restrictions during COVID-19 pandemic.

Late in 2019, China identified a new type of coronavirus, SARS-CoV-2, and due to its fast spread, the World Health Organisation (WHO) declared a pandemic named COVID-19. Some variants of this virus were detected, including the Delta, which caused new waves of infections. This work uses an extended version of a SIRD model that includes vaccination effects to measure the impact of the Delta variant in three countries: Germany, Israel and Brazil. The calibrated models were able to reproduce the dynamics of the above countries. In addition, hypothetical scenarios were simulated to quantify the impact of vaccination and mitigation policies during the Delta wave. The results showed that the model could reproduce the complex dynamics observed in the different countries. The estimated increase of transmission rate due to the Delta variant was highest in Israel (7.9), followed by Germany (2.7) and Brazil (1.5). These values may support the hypothesis that people immunised against COVID-19 may lose their defensive antibodies with time since Israel, Germany, and Brazil fully vaccinated half of the population in March, July, and October. The scenario to study the impact of vaccination revealed relative reductions in the total number of deaths between 30% and 250%; an absolute reduction of 300 thousand deaths in Brazil due to vaccination during the Delta wave. The second hypothetical scenario revealed that mitigation policies saved up to 300 thousand Brazilians; relative reductions in the total number of deaths between 24% and 120% in the three analysed countries. Therefore, the results suggest that both vaccination and mitigation policies were crucial in decreasing the spread and the number of deaths during the Delta wave.