SARS-CoV-2 booster vaccine dose significantly extends humoral immune response half-life beyond the primary series.

SARS-CoV-2 lipid nanoparticle mRNA vaccines continue to be administered as the predominant prophylactic measure to reduce COVID-19 disease pathogenesis. Quantifying the kinetics of the secondary immune response from subsequent doses beyond the primary series and understanding how dose-dependent immune waning kinetics vary as a function of age, sex, and various comorbidities remains an important question. We study anti-spike IgG waning kinetics in 152 individuals who received an mRNA-based primary series (first two doses) and a subset of 137 individuals who then received an mRNA-based booster dose. We find the booster dose elicits a 71-84% increase in the median Anti-S half life over that of the primary series. We find the Anti-S half life for both primary series and booster doses decreases with age. However, we stress that although chronological age continues to be a good proxy for vaccine-induced humoral waning, immunosenescence is likely not the mechanism, rather, more likely the mechanism is related to the presence of noncommunicable diseases, which also accumulate with age, that affect immune regulation. We are able to independently reproduce recent observations that those with pre-existing asthma exhibit a stronger primary series humoral response to vaccination than compared to those that do not, and further, we find this result is sustained for the booster dose. Finally, via a single-variate Kruskal-Wallis test we find no difference between male and female humoral decay kinetics, however, a multivariate approach utilizing  Least Absolute Shrinkage and Selection Operator (LASSO) regression for feature selection reveals a statistically significant (p < 1 × 10 - 3 ), albeit small, bias in favour of longer-lasting humoral immunity amongst males.

Climate-dependent effectiveness of nonpharmaceutical interventions on COVID-19 mitigation.

Environmental factors have a significant impact on the transmission of infectious diseases. Existing results show that the novel coronavirus can persist outside the host. We propose a susceptible-exposed-presymptomatic-infectious-asymptomatic-recovered-susceptible (SEPIARS) model with a vaccination compartment and indirect incidence to explore the effect of environmental conditions, temperature and humidity, on the transmission of the SARS-CoV-2 virus. Using climate data and daily confirmed cases data in two Canadian cities with different atmospheric conditions, we evaluate the mortality rates of the SARS-CoV-2 virus and further estimate the transmission rates by the inverse method, respectively. The numerical results show that high temperature or humidity can be helpful in mitigating the spread of COVID-19 during the warm summer months. Our findings verify that nonpharmaceutical interventions are less effective if the virus can persist for a long time on surfaces. Based on climate data, we can forecast the transmission rate and the infection cases up to four weeks in the future by a generalized boosting machine learning model.

The importance of quarantine: modelling the COVID-19 testing process.

We incorporate the disease state and testing state into the formulation of a COVID-19 epidemic model. For this model, the basic reproduction number is identified and its dependence on model parameters related to the testing process and isolation efficacy is discussed. The relations between the basic reproduction number, the final epidemic and peak sizes, and the model parameters are further explored numerically. We find that fast test reporting does not always benefit the control of the COVID-19 epidemic if good quarantine while awaiting test results is implemented. Moreover, the final epidemic and peak sizes do not always increase along with the basic reproduction number. Under some circumstances, lowering the basic reproduction number increases the final epidemic and peak sizes. Our findings suggest that properly implementing isolation for individuals who are waiting for their testing results would lower the basic reproduction number as well as the final epidemic and peak sizes.

Pandemic modelling for regions implementing an elimination strategy.

During the COVID-19 pandemic, some countries, such as Australia, China, Iceland, New Zealand, Thailand, and Vietnam successfully implemented an elimination strategy, enacting strict border control and periods of lockdowns to end community transmission. Atlantic Canada and Canada's territories implemented similar policies, and reported long periods with no community cases. In Newfoundland and Labrador (NL), Nova Scotia, and Prince Edward Island a median of 80% or more of daily reported cases were travel-related from July 1, 2020 to May 31, 2021. With increasing vaccination coverage, it may be appropriate to exit an elimination strategy, but most existing epidemiological frameworks are applicable only to situations where most cases occur in the community, and are not appropriate for regions that have implemented an elimination strategy. To inform the pandemic response in regions that are implementing an elimination strategy, we extend importation modelling to consider post-arrival travel restrictions, and pharmaceutical and non-pharmaceutical interventions in the local community. We find that shortly after the Omicron variant had begun spreading in Canada, the expected daily number of spillovers, infections spread to NL community members from travellers and their close contacts, was higher than any time previously in the pandemic. By December 24, 2021, the expected number of spillovers was 44% higher than the previous high, which occurred in late July 2021 shortly after travel restrictions were first relaxed. We develop a method to assess the characteristics of potential future community outbreaks in regions that are implementing an elimination strategy. We apply this method to predict the effect of variant and vaccination coverage on the size of hypothetical community outbreaks in Mount Pearl, a suburb of the St. John's metropolitan area in NL. Our methodology can be used to evaluate alternative plans to relax public health restrictions when vaccine coverage is high in regions that have implemented an elimination strategy. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Assessing transmission risks and control strategy for monkeypox as an emerging zoonosis in a metropolitan area.

To model the spread of monkeypox (MPX) in a metropolitan area for assessing the risk of possible outbreaks, and identifying essential public health measures to contain the virus spread. The animal reservoir is the key element in the modeling of zoonotic disease. Using a One Health approach, we model the spread of the MPX virus in humans considering potential animal hosts such as rodents (e.g., rats, mice, squirrels, chipmunks, etc.) and emphasize their role and transmission of the virus in a high-risk group, including gay and bisexual men-who-have-sex-with-men (gbMSM). From model and sensitivity analysis, we identify key public health factors and present scenarios under different transmission assumptions. We find that the MPX virus may spill over from gbMSM high-risk groups to broader populations if the efficiency of transmission increases in the higher-risk group. However, the risk of outbreak can be greatly reduced if at least 65% of symptomatic cases can be isolated and their contacts traced and quarantined. In addition, infections in an animal reservoir will exacerbate MPX transmission risk in the human population. Regions or communities with a higher proportion of gbMSM individuals need greater public health attention. Tracing and quarantine (or "effective quarantine" by postexposure vaccination) of contacts with MPX cases in high-risk groups would have a significant effect on controlling the spreading. Also, monitoring for animal infections would be prudent.

Modeling vaccination and control strategies for outbreaks of monkeypox at gatherings.

Background: The monkeypox outbreak in non-endemic countries in recent months has led the World Health Organization (WHO) to declare a public health emergency of international concern (PHEIC). It is thought that festivals, parties, and other gatherings may have contributed to the outbreak. Methods: We considered a hypothetical metropolitan city and modeled the transmission of the monkeypox virus in humans in a high-risk group (HRG) and a low-risk group (LRG) using a Susceptible-Exposed-Infectious-Recovered (SEIR) model and incorporated gathering events. Model simulations assessed how the vaccination strategies combined with other public health measures can contribute to mitigating or halting outbreaks from mass gathering events. Results: The risk of a monkeypox outbreak was high when mass gathering events occurred in the absence of public health control measures. However, the outbreaks were controlled by isolating cases and vaccinating their close contacts. Furthermore, contact tracing, vaccinating, and isolating close contacts, if they can be implemented, were more effective for the containment of monkeypox transmission during summer gatherings than a broad vaccination campaign among HRG, when accounting for the low vaccination coverage in the overall population, and the time needed for the development of the immune responses. Reducing the number of attendees and effective contacts during the gathering could also prevent a burgeoning outbreak, as could restricting attendance through vaccination requirements. Conclusion: Monkeypox outbreaks following mass gatherings can be made less likely with some restrictions on either the number and density of attendees in the gathering or vaccination requirements. The ring vaccination strategy inoculating close contacts of confirmed cases may not be enough to prevent potential outbreaks; however, mass gatherings can be rendered less risky if that strategy is combined with public health measures, including identifying and isolating cases and contact tracing. Compliance with the community and promotion of awareness are also indispensable to containing the outbreak.

Mathematical modelling of vaccination rollout and NPIs lifting on COVID-19 transmission with VOC: a case study in Toronto, Canada.

BACKGROUND: Since December 2020, public health agencies have implemented a variety of vaccination strategies to curb the spread of SARS-CoV-2, along with pre-existing Nonpharmaceutical Interventions (NPIs). Initial strategies focused on vaccinating the elderly to prevent hospitalizations and deaths, but with vaccines becoming available to the broader population, it became important to determine the optimal strategy to enable the safe lifting of NPIs while avoiding virus resurgence. METHODS: We extended the classic deterministic SIR compartmental disease-transmission model to simulate the lifting of NPIs under different vaccine rollout scenarios. Using case and vaccination data from Toronto, Canada between December 28, 2020, and May 19, 2021, we estimated transmission throughout past stages of NPI escalation/relaxation to compare the impact of lifting NPIs on different dates on cases, hospitalizations, and deaths, given varying degrees of vaccine coverages by 20-year age groups, accounting for waning immunity. RESULTS: We found that, once coverage among the elderly is high enough (80% with at least one dose), the main age groups to target are 20-39 and 40-59 years, wherein first-dose coverage of at least 70% by mid-June 2021 is needed to minimize the possibility of resurgence if NPIs are to be lifted in the summer. While a resurgence was observed for every scenario of NPI lifting, we also found that under an optimistic vaccination coverage (70% coverage by mid-June, along with postponing reopening from August 2021 to September 2021) can reduce case counts and severe outcomes by roughly 57% by December 31, 2021. CONCLUSIONS: Our results suggest that focusing the vaccination strategy on the working-age population can curb the spread of SARS-CoV-2. However, even with high vaccination coverage in adults, increasing contacts and easing protective personal behaviours is not advisable since a resurgence is expected to occur, especially with an earlier reopening.

Efficacy of a "stay-at-home" policy on SARS-CoV-2 transmission in Toronto, Canada: a mathematical modelling study.

BACKGROUND: Globally, nonpharmaceutical interventions for COVID-19, including stay-at-home policies, limitations on gatherings and closure of public spaces, are being lifted. We explored the effect of lifting a stay-at-home policy on virus resurgence under different conditions. METHODS: Using confirmed case data from Toronto, Canada, between Feb. 24 and June 24, 2020, we ran a compartmental model with household structure to simulate the impact of the stay-at-home policy considering different levels of compliance. We estimated threshold values for the maximum number of contacts, probability of transmission and testing rates required for the safe reopening of the community. RESULTS: After the implementation of the stay-at-home policy, the contact rate outside the household fell by 39% (from 11.58 daily contacts to 7.11). The effective reproductive number decreased from 3.56 (95% confidence interval [CI] 3.02-4.14) on Mar. 12 to 0.84 (95% CI 0.79-0.89) on May 6. Strong adherence to stay-at-home policies appeared to prevent SARS-CoV-2 resurgence, but extending the duration of stay-at-home policies beyond 2 months had little added effect on cumulative cases (25 958 for 65 days of a stay-at-home policy and 23 461 for 95 days, by July 2, 2020) and deaths (1404 for 65 days and 1353 for 95 days). To avoid a resurgence, the average number of contacts per person per day should be kept below 9, with strict nonpharmaceutical interventions in place. INTERPRETATION: Our study demonstrates that the stay-at-home policy implemented in Toronto in March 2020 had a substantial impact on mitigating the spread of SARS-CoV-2. In the context of the early pandemic, before the emergence of variants of concern, reopening schools and workplaces was possible only with other nonpharmaceutical interventions in place.

Stochastic dispersal increases the rate of upstream spread: A case study with green crabs on the northwest Atlantic coast.

Dispersal heterogeneity is an important process that can compensate for downstream advection, enabling aquatic organisms to persist or spread upstream. Our main focus was the effect of year-to-year variation in larval dispersal on invasion spread rate. We used the green crab, Carcinus maenas, as a case study. This species was first introduced over 200 years ago to the east coast of North America, and once established has maintained a relatively consistent spread rate against the dominant current. We used a stage-structured, integro-difference equation model that couples a demographic matrix for population growth and dispersal kernels for spread of individuals within a season. The kernel describing larval dispersal, the main dispersive stage, was mechanistically modeled to include both drift and settlement rate components. It was parameterized using a 3-dimensional hydrodynamic model of the Gulf of St Lawrence, which enabled us to incorporate larval behavior, namely vertical swimming. Dispersal heterogeneity was modeled at two temporal scales: within the larval period (months) and over the adult lifespan (years). The kernel models variation within the larval period. To model the variation among years, we allowed the kernel parameters to vary by year. Results indicated that when dispersal parameters vary with time, knowledge of the time-averaged dispersal process is insufficient for determining the upstream spread rate of the population. Rather upstream spread is possible over a number of years when incorporating the yearly variation, even when there are only a few "good years" featured by some upstream dispersal among many "bad years" featured by only downstream dispersal. Accounting for annual variations in dispersal in population models is important to enhance understanding of spatial dynamics and population spread rates. Our developed model also provides a good platform to link the modeling of larval behavior and demography to large-scale hydrodynamic models.

Transient spatio-temporal dynamics of a diffusive plant-herbivore system with Neumann boundary conditions.

In many existing predator-prey or plant-herbivore models, the numerical response is assumed to be proportional to the functional response. In this paper, without such an assumption, we consider a diffusive plant-herbivore system with Neumann boundary conditions. Besides stability of spatially homogeneous steady states, we also derive conditions for the occurrence of Hopf bifurcation and steady-state bifurcation and provide geometrical methods to locate the bifurcation values. We numerically explore the complex transient spatio-temporal behaviours induced by these bifurcations. A large variety of different types of transient behaviours including oscillations in one or both of space and time are observed.

Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions.

In this paper, we study a diffusive plant-herbivore system with homogeneous and nonhomogeneous Dirichlet boundary conditions. Stability of spatially homogeneous steady states is established. We also derive conditions ensuring the occurrence of Hopf bifurcation and steady state bifurcation. Interesting transient spatio-temporal behaviors including oscillations in one or both of space and time are observed through numerical simulations.

Delay induced stability switch, multitype bistability and chaos in an intraguild predation model.

In many predator-prey models, delay has a destabilizing effect and induces oscillations; while in many competition models, delay does not induce oscillations. By analyzing a rather simple delayed intraguild predation model, which combines both the predator-prey relation and competition, we show that delay in intraguild predation models promotes very complex dynamics. The delay can induce stability switches exhibiting a destabilizing role as well as a stabilizing role. It is shown that three types of bistability are possible: one stable equilibrium coexists with another stable equilibrium (node-node bistability); one stable equilibrium coexists with a stable periodic solution (node-cycle bistability); one stable periodic solution coexists with another stable periodic solution (cycle-cycle bistability). Numerical simulations suggest that delay can also induce chaos in intraguild predation models.

Sustained and transient oscillations and chaos induced by delayed antiviral immune response in an immunosuppressive infection model.

Sustained and transient oscillations are frequently observed in clinical data for immune responses in viral infections such as human immunodeficiency virus, hepatitis B virus, and hepatitis C virus. To account for these oscillations, we incorporate the time lag needed for the expansion of immune cells into an immunosuppressive infection model. It is shown that the delayed antiviral immune response can induce sustained periodic oscillations, transient oscillations and even sustained aperiodic oscillations (chaos). Both local and global Hopf bifurcation theorems are applied to show the existence of periodic solutions, which are illustrated by bifurcation diagrams and numerical simulations. Two types of bistability are shown to be possible: (i) a stable equilibrium can coexist with another stable equilibrium, and (ii) a stable equilibrium can coexist with a stable periodic solution.

Pandemic influenza: Modelling and public health perspectives.

We describe the application of mathematical models in the study of disease epidemics with particular focus on pandemic influenza. We outline the general mathematical approach and the complications arising from attempts to apply it for disease outbreak management in a real public health context.

Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic.

Since the discovery of HIV/AIDS there have been numerous mathematical models proposed to explain the epidemic of the disease and to evaluate possible control measures. In particular, several recent studies have looked at the potential impact of condom usage on the epidemic [1, 2, 3, 4]. We develop a simple model for HIV/AIDS, and investigate the effectiveness of condoms as a possible control strategy. We show that condoms can greatly reduce the number of outbreaks and the size of the epidemic. However, the necessary condom usage levels are much higher than the current estimates. We conclude that condoms alone will not be sufficient to halt the epidemic in most populations unless current estimates of the transmission probabilities are high. Our model has only five independent parameters, which allows for a complete analysis. We show that the assumptions of mass action and standard incidence provide similar results, which implies that the results of the simpler mass action model can be used as a good first approximation to the peak of the epidemic.

Age of infection epidemic models with heterogeneous mixing.

We extend the age of infection epidemic models to populations divided into an arbitrary number of subgroups and derive a set of final size relations if there are no disease deaths. If there are disease deaths, the final size relations are inequalities, but it is possible to obtain bounds for the epidemic size in terms of the final size for the corresponding model without disease deaths and the disease death rates. If the mixing is proportionate, we obtain an explicit expression for the reproduction number of the model. The heterogeneous mixing age of infection epidemic model is a unified form that includes general compartmental structures and arbitrary distributions of stay in compartments as well as heterogeneity of mixing.

Potato field colonization by low-density populations of Colorado potato beetle as a function of crop rotation distance.

Monitoring of 10 and 12 commercial potato, Solanum tuberosum L., fields in 2004 and 2005, respectively, confirmed for a low-density population of Colorado potato beetle, Leptinotarsa decemlineata (Say), that potato fields nearest to the previous year's potato fields are significantly more colonized by this beetle than more distant fields. This pattern is partially explained by the presence of a reservoir of colonizers estimated at 35% of the season-long colonizing population in 2004 and 2005. These beetles, which emerged before potato plants broke the ground, were ready to establish themselves on nearby potato plants. The colonizing Colorado potato beetles dispersed within the maximum range of 1.5 km over a season, and the colonization risk for the new crop decreased with distance from the previous year's crop. There was no evidence that rotation distance delayed colonization. In terms of pest management, although the findings confirm that only long 1.5-km rotations can prevent Colorado potato beetle colonization, they also demonstrate that short rotations of 100 m or more can make substantial contributions to pest management programs for low-density beetle populations.

A model for influenza with vaccination and antiviral treatment.

Compartmental models for influenza that include control by vaccination and antiviral treatment are formulated. Analytic expressions for the basic reproduction number, control reproduction number and the final size of the epidemic are derived for this general class of disease transmission models. Sensitivity and uncertainty analyses of the dependence of the control reproduction number on the parameters of the model give a comparison of the various intervention strategies. Numerical computations of the deterministic models are compared with those of recent stochastic simulation influenza models. Predictions of the deterministic compartmental models are in general agreement with those of the stochastic simulation models.

Role of incidence function in vaccine-induced backward bifurcation in some HIV models.

The phenomenon of backward bifurcation in disease models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity, has important implications for disease control. In such a scenario, the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, condition for disease elimination. This paper addresses the role of the choice of incidence function in a vaccine-induced backward bifurcation in HIV models. Several examples are given where backward bifurcations occur using standard incidence, but not with their equivalents that employ mass action incidence. Furthermore, this result is independent of the type of vaccination program adopted. These results emphasize the need for further work on the incidence functions used in HIV models.