Modeling COVID-19 dynamic using a two-strain model with vaccination.

Multiple strains of the SARS-CoV-2 have arisen and jointly influence the trajectory of the coronavirus disease (COVID-19) pandemic. However, current models rarely account for this multi-strain dynamics and their different transmission rate and response to vaccines. We propose a new mathematical model that accounts for two virus variants and the deployment of a vaccination program. To demonstrate utility, we applied the model to determine the control reproduction number ( R c ) and the per day infection, death and recovery rates of each strain in the US pandemic. The model dynamics predicted the rise of the alpha variant and shed light on potential impact of the delta variant in 2021. We obtained the minimum percentage of fully vaccinated individuals to reduce the spread of the variants in combination with other intervention strategies to deaccelerate the rise of a multi-strain pandemic.

Boolean modeling reveals that cyclic attractors in macrophage polarization serve as reservoirs of states to balance external perturbations from the tumor microenvironment.

Cyclic attractors generated from Boolean models may explain the adaptability of a cell in response to a dynamical complex tumor microenvironment. In contrast to this idea, we postulate that cyclic attractors in certain cases could be a systemic mechanism to face the perturbations coming from the environment. To justify our conjecture, we present a dynamic analysis of a highly curated transcriptional regulatory network of macrophages constrained into a cancer microenvironment. We observed that when M1-associated transcription factors (STAT1 or NF-κB) are perturbed and the microenvironment balances to a hyper-inflammation condition, cycle attractors activate genes whose signals counteract this effect implicated in tissue damage. The same behavior happens when the M2-associated transcription factors are disturbed (STAT3 or STAT6); cycle attractors will prevent a hyper-regulation scenario implicated in providing a suitable environment for tumor growth. Therefore, here we propose that cyclic macrophage phenotypes can serve as a reservoir for balancing the phenotypes when a specific phenotype-based transcription factor is perturbed in the regulatory network of macrophages. We consider that cyclic attractors should not be simply ignored, but it is necessary to carefully evaluate their biological importance. In this work, we suggest one conjecture: the cyclic attractors can serve as a reservoir to balance the inflammatory/regulatory response of the network under external perturbations.

Sensitivity theorems of a model of multiple imperfect vaccines for COVID-19.

In response to the ongoing pandemic of COVID-19, several companies across the world have proposed a wide variety of vaccines of different mechanisms of action. As a consequence, a new scenario of multiple imperfect vaccines against the SARS-CoV-2 arose. Mathematical modeling needs to consider this complex situation with different vaccines, some of them with two required doses. Using compartmental models we can simplify, simulate and most importantly, answer questions related to the development of the outbreak and the vaccination campaign. We present a model that addresses the current situation of COVID-19 and vaccination. Two important questions were considered in this paper: are more vaccines useful to reduce the spread of the coronavirus? How can we know if the vaccination campaign is sufficient? Two sensitivity criteria are helpful to answer these questions. The first criterion is the Multiple Vaccination Theorem, which indicates whether a vaccine is giving a positive or negative impact on the reproduction number. The second result (Insufficiency Theorem) provides a condition to answer the second question. Finally, we fitted the parameters with data and discussed the empirical results of six countries: Israel, Germany, the Czech Republic, Portugal, Italy, and Lithuania.

Modeling COVID-19 dynamic using a two-strain model with vaccination

Multiple strains of the SARS-CoV-2 have arisen and jointly influence the trajectory of the coronavirus disease (COVID-19) pandemic. However, current models rarely account for this multi-strain dynamics and their different transmission rate and response to vaccines. We propose a new mathematical model that accounts for two virus variants and the deployment of a vaccination program. To demonstrate utility, we applied the model to determine the control reproduction number