COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat for human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. Considering different starting times of infection, mathematical models are proposed to represent SARS-CoV-2 dynamics in infected patients. Based on the target cell limited model, the within-host reproductive number for SARS-CoV-2 is consistent with the broad values of human influenza infection. The best model to fit the data was including immune cell response, which suggests a slow immune response peaking between 5 to 10 days post-onset of symptoms. The model with the eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, all models predict that SARS-CoV-2 may replicate very slowly in the first days after infection, and viral load could be below detection levels during the first 4 days post infection. A quantitative comprehension of SARS-CoV-2 dynamics and the estimation of standard parameters of viral infections is the key contribution of this pioneering work. These models can serve for future evaluation of control theoretical approaches to tailor new potential drugs against COVID-19.

SUMMARYThis paper has been motivated by the problem of viral mutation in HIV infection. Under simplifying assumptions, viral mutation treatment dynamics can be viewed as a positive switched linear system. Using linear co-positive Lyapunov functions, results for the synthesis of stabilizing, guaranteed performance and optimal control laws for switched linear systems are presented. These results are then applied to a simplified human immunodeficiency viral mutation model. The optimal switching control law is compared with the law obtained through an easily computable guaranteed cost function. Simulation results show the effectiveness of these methods.

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization.

In patients who are receiving prolonged antiretroviral treatment (ART), HIV can persist within a small pool of long-lived resting memory CD4+ T cells infected with integrated latent virus. This latent reservoir involves distinct memory subsets. Here we provide results that suggest a progressive reduction of the size of the blood latent reservoir around a core of less-differentiated memory subsets (central memory and stem cell-like memory (TSCM) CD4+ T cells). This process appears to be driven by the differences in initial sizes and decay rates between latently infected memory subsets. Our results also suggest an extreme stability of the TSCM sub-reservoir, the size of which is directly related to cumulative plasma virus exposure before the onset of ART, stressing the importance of early initiation of effective ART. The presence of these intrinsic dynamics within the latent reservoir may have implications for the design of optimal HIV therapeutic purging strategies.