The emergence of a virus variant: dynamics of a competition model with cross-immunity time-delay validated by wastewater surveillance data for COVID-19

Modeling the effects of cross immunity and control measures on competitive dynamics of SARS-CoV-2 variants in the USA, UK, and Brazil

Mutation in the SARS-CoV-2 virus may lead to the evolution of new variants. The dynamics of these variants varied among countries. Identification of the governing factors responsible for distinctions in their dynamics is important for preparedness against future severe variants. This study investigates the impact of cross immunity and control measures on the competition dynamics of the Alpha, Gamma, Delta, and Omicron variants. The following questions are addressed using an n-strain deterministic model: (i) Why do a few variants fail to cause a wave even after winning the competition? (ii) In what scenarios a new variant cannot replace the previous one? The model is fitted and cross-validated with the data of COVID-19 and its variants for the USA, UK, and Brazil. The model analysis highlights implementations of the following measures against any deadlier future variant: (i) an effective population-wide cross-immunity from less lethal strains and (ii) strain-specific vaccines targeting the novel variant. The system exhibits a fascinating dynamical behavior known as an endemic bubble due to Hopf bifurcation. It is observed that the actual situation in which Omicron won the competition from Delta followed by no wave due to Delta may turn into a competitive periodic coexistence of two strains due to substantial disparity in fading rates of cross-immunity. Global sensitivity analysis is conducted to quantify uncertainties of model parameters. It is found that examining the impact of cross-immunity is as crucial as vaccination.

Post-recovery viral shedding shapes wastewater-based epidemiological inferences

BACKGROUND

The prolonged viral shedding from the gastrointestinal tract is well documented for numerous pathogens, including SARS-CoV-2. However, the impact of prolonged viral shedding on epidemiological inferences using wastewater data is not yet fully understood.

METHODS

To gain a better understanding of this phenomenon at the population level, we extended a wastewater-based modeling framework that integrates viral shedding dynamics, viral load data in wastewater, case report data, and an epidemic model.

RESULTS

Our results indicate that as an outbreak progresses, the viral load from recovered individuals gradually becomes predominant, surpassing that from the infectious population. This phenomenon leads to a dynamic relationship between model-inferred and reported daily incidence over the course of an outbreak. Sensitivity analyses on the duration and rate of viral shedding for recovered individuals reveal that accounting for this phenomenon can considerably advance prediction of transmission peak timing. Furthermore, extensive viral shedding from the recovered population toward the conclusion of an epidemic wave may overshadow viral signals from newly infected cases carrying emerging variants, which can delay the rapid recognition of emerging variants based on viral load.

CONCLUSIONS

These findings highlight the necessity of integrating post-recovery viral shedding to enhance the accuracy and utility of wastewater-based epidemiological analysis.

Age-structured modeling of COVID-19 dynamics: the role of treatment and vaccination in controlling the pandemic

In addition to non-pharmaceutical interventions, antiviral drugs and vaccination are considered as the optimal solutions to control and eliminate the COVID-19 pandemic. It is necessary to couple within-host and between-host models to investigate the impact of treatment and vaccination. Hence, we propose an age-structured model, where the infection age is used to link the within-host viral dynamics and the disease dynamics at the population level. We conduct a detailed analysis of the local and global dynamics of the model, and the threshold dynamics are completely determined by the basic reproduction number R 0 . Thus, the disease-free equilibrium is globally asymptotically stable and the disease eventually dies out whenR 0 < 1 ; the disease-free equilibrium is globally attractive whenR 0 = 1 ; the disease is uniformly persistent, and the unique endemic equilibrium is globally asymptotically stable whenR 0 > 1 . The numerical simulation quantitatively studies the impact of the within-host viral dynamics on between-host transmission dynamics. The results show that the combination of antiviral drugs and vaccines can play a key role in mitigating the spread of COVID-19, but it is challenging to eliminate COVID-19 alone. To achieve the complete elimination of COVID-19, we need highly effective antiviral drugs and near-universal vaccine coverage.

Wastewater-based epidemiology for COVID-19 surveillance and beyond: A survey

The pandemic of COVID-19 has imposed tremendous pressure on public health systems and social economic ecosystems over the past years. To alleviate its social impact, it is important to proactively track the prevalence of COVID-19 within communities. The traditional way to estimate the disease prevalence is to estimate from reported clinical test data or surveys. However, the coverage of clinical tests is often limited and the tests can be labor-intensive, requires reliable and timely results, and consistent diagnostic and reporting criteria. Recent studies revealed that patients who are diagnosed with COVID-19 often undergo fecal shedding of SARS-CoV-2 virus into wastewater, which makes wastewater-based epidemiology for COVID-19 surveillance a promising approach to complement traditional clinical testing. In this paper, we survey the existing literature regarding wastewater-based epidemiology for COVID-19 surveillance and summarize the current advances in the area. Specifically, we have covered the key aspects of wastewater sampling, sample testing, and presented a comprehensive and organized summary of wastewater data analytical methods. Finally, we provide the open challenges on current wastewater-based COVID-19 surveillance studies, aiming to encourage new ideas to advance the development of effective wastewater-based surveillance systems for general infectious diseases.

Wastewater-based Epidemiology for COVID-19 Surveillance and Beyond: A Survey

The pandemic of COVID-19 has imposed tremendous pressure on public health systems and social economic ecosystems over the past years. To alleviate its social impact, it is important to proactively track the prevalence of COVID-19 within communities. The traditional way to estimate the disease prevalence is to estimate from reported clinical test data or surveys. However, the coverage of clinical tests is often limited and the tests can be labor-intensive, requires reliable and timely results, and consistent diagnostic and reporting criteria. Recent studies revealed that patients who are diagnosed with COVID-19 often undergo fecal shedding of SARS-CoV-2 virus into wastewater, which makes wastewater-based epidemiology for COVID-19 surveillance a promising approach to complement traditional clinical testing. In this paper, we survey the existing literature regarding wastewater-based epidemiology for COVID-19 surveillance and summarize the current advances in the area. Specifically, we have covered the key aspects of wastewater sampling, sample testing, and presented a comprehensive and organized summary of wastewater data analytical methods. Finally, we provide the open challenges on current wastewater-based COVID-19 surveillance studies, aiming to encourage new ideas to advance the development of effective wastewater-based surveillance systems for general infectious diseases.

Jointly estimating epidemiological dynamics of Covid-19 from case and wastewater data in Aotearoa New Zealand

BACKGROUND

Timely and informed public health responses to infectious diseases such as COVID-19 necessitate reliable information about infection dynamics. The case ascertainment rate (CAR), the proportion of infections that are reported as cases, is typically much less than one and varies with testing practices and behaviours, making reported cases unreliable as the sole source of data. The concentration of viral RNA in wastewater samples provides an alternate measure of infection prevalence that is not affected by clinical testing, healthcare-seeking behaviour or access to care.

METHODS

We construct a state-space model with observed data of levels of SARS-CoV-2 in wastewater and reported case incidence and estimate the hidden states of the effective reproduction number, R, and CAR using sequential Monte Carlo methods.

RESULTS

We analyse data from 1 January 2022 to 31 March 2023 from Aotearoa New Zealand. Our model estimates that R peaks at 2.76 (95% CrI 2.20, 3.83) around 18 February 2022 and the CAR peaks around 12 March 2022. We calculate that New Zealand's second Omicron wave in July 2022 is similar in size to the first, despite fewer reported cases. We estimate that the CAR in the BA.5 Omicron wave in July 2022 is approximately 50% lower than in the BA.1/BA.2 Omicron wave in March 2022.

CONCLUSIONS

Estimating R, CAR, and cumulative number of infections provides useful information for planning public health responses and understanding the state of immunity in the population. This model is a useful disease surveillance tool, improving situational awareness of infectious disease dynamics in real-time.

A Nonlinear Delay Model for Metabolic Oscillations in Yeast Cells

We introduce two time-delay models of metabolic oscillations in yeast cells. Our model tests a hypothesis that the oscillations occur as multiple pathways share a limited resource which we equate to the number of available ribosomes. We initially explore a single-protein model with a constraint equation governing the total resource available to the cell. The model is then extended to include three proteins that share a resource pool. Three approaches are considered at constant delay to numerically detect oscillations. First, we use a spectral element method to approximate the system as a discrete map and evaluate the stability of the linearized system about its equilibria by examining its eigenvalues. For the second method, we plot amplitudes of the simulation trajectories in 2D projections of the parameter space. We use a history function that is consistent with published experimental results to obtain metabolic oscillations. Finally, the spectral element method is used to convert the system to a boundary value problem whose solutions correspond to approximate periodic solutions of the system. Our results show that certain combinations of total resource available and the time delay, lead to oscillations. We observe that an oscillation region in the parameter space is between regions admitting steady states that correspond to zero and constant production. Similar behavior is found with the three-protein model where all proteins require the same production time. However, a shift in the protein production rates peaks occurs for low available resource suggesting that our model captures the shared resource pool dynamics.

Making waves: Integrating wastewater surveillance with dynamic modeling to track and predict viral outbreaks

Wastewater surveillance has proved to be a valuable tool to track the COVID-19 pandemic. However, most studies using wastewater surveillance data revolve around establishing correlations and lead time relative to reported case data. In this perspective, we advocate for the integration of wastewater surveillance data with dynamic within-host and between-host models to better understand, monitor, and predict viral disease outbreaks. Dynamic models overcome emblematic difficulties of using wastewater surveillance data such as establishing the temporal viral shedding profile. Complementarily, wastewater surveillance data bypasses the issues of time lag and underreporting in clinical case report data, thus enhancing the utility and applicability of dynamic models. The integration of wastewater surveillance data with dynamic models can enhance real-time tracking and prevalence estimation, forecast viral transmission and intervention effectiveness, and most importantly, provide a mechanistic understanding of infectious disease dynamics and the driving factors. Dynamic modeling of wastewater surveillance data will advance the development of a predictive and responsive monitoring system to improve pandemic preparedness and population health.

A two-strain model of infectious disease spread with asymmetric temporary immunity periods and partial cross-immunity

We introduce a two-strain model with asymmetric temporary immunity periods and partial cross-immunity. We derive explicit conditions for competitive exclusion and coexistence of the strains depending on the strain-specific basic reproduction numbers, temporary immunity periods, and degree of cross-immunity. The results of our bifurcation analysis suggest that, even when two strains share similar basic reproduction numbers and other epidemiological parameters, a disparity in temporary immunity periods and partial or complete cross-immunity can provide a significant competitive advantage. To analyze the dynamics, we introduce a quasi-steady state reduced model which assumes the original strain remains at its endemic steady state. We completely analyze the resulting reduced planar hybrid switching system using linear stability analysis, planar phase-plane analysis, and the Bendixson-Dulac criterion. We validate both the full and reduced models with COVID-19 incidence data, focusing on the Delta (B.1.617.2), Omicron (B.1.1.529), and Kraken (XBB.1.5) variants. These numerical studies suggest that, while early novel strains of COVID-19 had a tendency toward dramatic takeovers and extinction of ancestral strains, more recent strains have the capacity for co-existence.