Mathematical modeling of the dynamics of COVID-19 variants of concern: Asymptotic and finite-time perspectives.

The COVID-19 pandemic has seen multiple waves, in part due to the implementation and relaxation of social distancing measures by the public health authorities around the world, and also caused by the emergence of new variants of concern (VOCs) of the SARS-Cov-2 virus. As the COVID-19 pandemic is expected to transition into an endemic state, how to manage outbreaks caused by newly emerging VOCs has become one of the primary public health issues. Using mathematical modeling tools, we investigated the dynamics of VOCs, both in a general theoretical framework and based on observations from public health data of past COVID-19 waves, with the objective of understanding key factors that determine the dominance and coexistence of VOCs. Our results show that the transmissibility advantage of a new VOC is a main factor for it to become dominant. Additionally, our modeling study indicates that the initial number of people infected with the new VOC plays an important role in determining the size of the epidemic. Our results also support the evidence that public health measures targeting the newly emerging VOC taken in the early phase of its spread can limit the size of the epidemic caused by the new VOC (Wu et al., 2139Wu, Scarabel, Majeed, Bragazzi, & Orbinski, ; Wu et al., 2021).

Modeling the Effects of Latency Reversing Drugs During HIV-1 and SIV Brain Infection with Implications for the "Shock and Kill" Strategy.

Combination antiretroviral therapy (cART) has greatly increased life expectancy for human immunodeficiency virus-1 (HIV-1)-infected patients. Even given the remarkable success of cART, the virus persists in many different cells and tissues. The presence of viral reservoirs represents a major obstacle to HIV-1 eradication. These viral reservoirs contain latently infected long-lived cells. The "Shock and Kill" therapeutic strategy aims to reactivate latently infected cells by latency reversing agents (LRAs) and kill these reactivated cells by strategies involving the host immune system. The brain is a natural anatomical reservoir for HIV-1 infection. Brain macrophages, including microglia and perivascular macrophages, display productive HIV-1 infection. A mathematical model was used to analyze the dynamics of latently and productively infected brain macrophages during viral infection and this mathematical model enabled prediction of the effects of LRAs applied to the "Shock and Kill" strategy in the brain. The model was calibrated using reported data from simian immunodeficiency virus (SIV) studies. Our model produces the overarching observation that effective cART can suppress productively infected brain macrophages but leaves a residual latent viral reservoir in brain macrophages. In addition, our model demonstrates that there exists a parameter regime wherein the "Shock and Kill" strategy can be safe and effective for SIV infection in the brain. The results indicate that the "Shock and Kill" strategy can restrict brain viral RNA burden associated with severe neuroinflammation and can lead to the eradication of the latent reservoir of brain macrophages.

Why is it difficult to accurately predict the COVID-19 epidemic?

Since the COVID-19 outbreak in Wuhan City in December of 2019, numerous model predictions on the COVID-19 epidemics in Wuhan and other parts of China have been reported. These model predictions have shown a wide range of variations. In our study, we demonstrate that nonidentifiability in model calibrations using the confirmed-case data is the main reason for such wide variations. Using the Akaike Information Criterion (AIC) for model selection, we show that an SIR model performs much better than an SEIR model in representing the information contained in the confirmed-case data. This indicates that predictions using more complex models may not be more reliable compared to using a simpler model. We present our model predictions for the COVID-19 epidemic in Wuhan after the lockdown and quarantine of the city on January 23, 2020. We also report our results of modeling the impacts of the strict quarantine measures undertaken in the city after February 7 on the time course of the epidemic, and modeling the potential of a second outbreak after the return-to-work in the city.

Bayesian inference for dynamical systems.

Bayesian inference is a common method for conducting parameter estimation for dynamical systems. Despite the prevalent use of Bayesian inference for performing parameter estimation for dynamical systems, there is a need for a formalized and detailed methodology. This paper presents a comprehensive methodology for dynamical system parameter estimation using Bayesian inference and it covers utilizing different distributions, Markov Chain Monte Carlo (MCMC) sampling, obtaining credible intervals for parameters, and prediction intervals for solutions. A logistic growth example is given to illustrate the methodology.

Modeling brain lentiviral infections during antiretroviral therapy in AIDS.

Understanding HIV-1 replication and latency in different reservoirs is an ongoing challenge in the care of patients with HIV/AIDS. A mathematical model was created to describe and predict the viral dynamics of HIV-1 and SIV infection within the brain during effective combination antiretroviral therapy (cART). The mathematical model was formulated based on the biology of lentiviral infection of brain macrophages and used to describe the dynamics of transmission and progression of lentiviral infection in brain. Based on previous reports quantifying total viral DNA levels in brain from HIV-1 and SIV infections, estimates of integrated proviral DNA burden were made, which were used to calibrate the mathematical model predicting viral accrual in brain macrophages from primary infection. The annual rate at which susceptible brain macrophages become HIV-1 infected was estimated to be 2.90×10-7-4.87×10-6 per year for cART-treated HIV/AIDS patients without comorbid neurological disorders. The transmission rate for SIV infection among untreated macaques was estimated to be 5.30×10-6-1.37×10-5 per year. An improvement in cART effectiveness (1.6-48%) would suppress HIV-1 infection in patients without neurological disorders. Among patients with advanced disease, a substantial improvement in cART effectiveness (70%) would eradicate HIV-1 provirus from the brain within 3-32 (interquartile range 3-9) years in patients without neurological disorders, whereas 4-51 (interquartile range 4-16) years of efficacious cART would be required for HIV/AIDS patients with comorbid neurological disorders. HIV-1 and SIV provirus burdens in the brain increase over time. A moderately efficacious antiretroviral therapy regimen could eradicate HIV-1 infection in the brain that was dependent on brain macrophage lifespan and the presence of neurological comorbidity.