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COVID-19 is a global pandemic leading high death tolls worldwide day by day. Clinical evidence suggests that COVID-19 patients can be classified as non-severe, severe and critical cases. In particular, studies have highlighted the relationship between the lymphopenia and the severity of the illness, where CD8+T cells have the lowest levels in critical cases. In this work, we aim to elucidate the key parameters that define the course of the disease deviating from severe to critical case. To this end, several mathematical models are proposed to represent the dynamic of the immune response in patients with SARS-CoV-2 infection. The best model had a good fit to reported experimental data, and in accordance with values found in the literature. Our results suggest that a rapid proliferation of CD8+T cells is decisive in the severity of the disease.

The novel coronavirus SARS-CoV-2 has paralysed our societies, leading to self isolation and quarantine for several days. As the 10th most populated country in the world, Mexico is on a major threat by COVID-19 due to the limitations of intensive care capacities, and a total of about 1.5 hospital beds for every 1000 citizens. In this paper, we projected different scenarios to evaluate sharp or gradual quarantine lifting strategies, however, even in the hypothetical scenario that Mexico would continue with full confinement, hospitals would be reaching the maximum capacity of hospital bed occupancy. Mexican government is planning to relax the strict social distancing regulations on 1 June 2020, however, epidemic rebound risks are latent.Our results suggest that lifting social confinement needs to be gradually sparse while maintaining a decentralized region strategy among the Mexican states. To substantially lower the number of infections, predictions highlight that the elderly should remain in social confinement (approximately 11.3% of the population); the confined working class (roughly 27% of the population) must gradually return in at least four parts in consecutive months; and to the last the return of students to schools (about 21.7%). As the epidemic progresses, de-confinement strategies need to be continuously re-adjusting with the new pandemic data. Assuming the most optimistic scenario by our predictions, the smallest number of new COVID-19 cases, Mexico would require at least a 3 fold increase in hospital capacities dedicated for COVID-19. Furthermore, to observe the real dimension of the epidemic, Mexico would need to increase to at least 18 samples per 1000 people, currently is only 0.6 per 1000.All mathematical models, including ours, are only a possibility of many of the future, however, the different scenarios that were developed here highlight that a gradual decentralized region de-confinement with a significant increase in healthcare capacities is paramount to avoid a high death toll in Mexico.