Mathematical modeling of COVID-19 in British Columbia: An age-structured model with time-dependent contact rates

Dynamics of infectious disease mathematical model through unsupervised stochastic neural network paradigm

The viruses has spread globally and have been impacted lives of people socially and economically, which causes immense suffering throughout the world. Thousands of people died and millions of illnesses were brought, by the outbreak worldwide. In order to control the coronavirus pandemic, mathematical modeling proved to be an invaluable tool for analyzing and determining the potential and severity of the illness. This work proposed and assessed a deterministic six-compartment model with a novel stochastic neural network. The significance of the proposed model was demonstrated by numerical simulation in which the results are agreed with sensitivity analysis. Furthermore, the efficacy of stochastic neural network has been proven with the help of numerical simulations. Some investigations have been conducted through graphs and tables that how the vaccination process is helpful to minimize stress in society. The numerical simulations also focused on preventing the community-wide spread of the disease. The lowest residual errors have been achieved by our proposed stochastic neural network and compared with numerical solvers to assess the accuracy and robustness of the proposed approach.

A vaccination-based COVID-19 model: Analysis and prediction using Hamiltonian Monte Carlo

Compartmental models have emerged as robust computational frameworks and have yielded remarkable success in the fight against COVID-19. This study proposes a vaccination-based compartmental model for COVID-19 transmission dynamics. The model reflects the specific stages of COVID-19 infection and integrates a vaccination strategy, allowing for a comprehensive analysis of how vaccination rates influence the disease spread. We fit this model to daily confirmed COVID-19 cases in Tennessee, United States of America (USA), from June 4 to November 26, 2021, in a Bayesian inference approach using the Hamiltonian Monte Carlo (HMC) algorithm. First, excluding vaccination dynamics from the model, we estimated key epidemiological parameters like infection, recovery, and disease-induced death rates. This analysis yielded a basic reproduction number (R 0 ) of 1.5. Second, we incorporated vaccination dynamics and estimated the vaccination rate for three vaccines: 0.0051 per day for both Pfizer and Moderna and 0.0059 per day for Janssen. The fitted curves show reductions in the epidemic peak for all three vaccines. Pfizer and Moderna vaccines bring the peak down from 8,029 infected cases to 5,616 infected cases, while the Janssen vaccine reduces it, to 6,493 infected cases. Simulations of the model by varying the vaccination rate and vaccine efficacy were performed. A highly effective vaccine (95% efficacy) with a daily vaccination rate of 0.006 halved COVID-19 infections, reducing cases from 8,029 to around 4,000. The results also show that the model's prediction accuracy for new observations improves with the number of observed data used to train the model.

Canada's provincial COVID-19 pandemic modelling efforts: A review of mathematical models and their impacts on the responses

SETTING

Mathematical modelling played an important role in the public health response to COVID-19 in Canada. Variability in epidemic trajectories, modelling approaches, and data infrastructure across provinces provides a unique opportunity to understand the factors that shaped modelling strategies.

INTERVENTION

Provinces implemented stringent pandemic interventions to mitigate SARS-CoV-2 transmission, considering evidence from epidemic models. This study aimed to summarize provincial COVID-19 modelling efforts. We identified modelling teams working with provincial decision-makers, through referrals and membership in Canadian modelling networks. Information on models, data sources, and knowledge translation were abstracted using standardized instruments.

OUTCOMES

We obtained information from six provinces. For provinces with sustained community transmission, initial modelling efforts focused on projecting epidemic trajectories and healthcare demands, and evaluating impacts of proposed interventions. In provinces with low community transmission, models emphasized quantifying importation risks. Most of the models were compartmental and deterministic, with projection horizons of a few weeks. Models were updated regularly or replaced by new ones, adapting to changing local epidemic dynamics, pathogen characteristics, vaccines, and requests from public health. Surveillance datasets for cases, hospitalizations and deaths, and serological studies were the main data sources for model calibration. Access to data for modelling and the structure for knowledge translation differed markedly between provinces.

IMPLICATION

Provincial modelling efforts during the COVID-19 pandemic were tailored to local contexts and modulated by available resources. Strengthening Canadian modelling capacity, developing and sustaining collaborations between modellers and governments, and ensuring earlier access to linked and timely surveillance data could help improve pandemic preparedness.

Understanding the impact of mobility on COVID-19 spread: A hybrid gravity-metapopulation model of COVID-19

The outbreak of the severe acute respiratory syndrome coronavirus 2 started in Wuhan, China, towards the end of 2019 and spread worldwide. The rapid spread of the disease can be attributed to many factors including its high infectiousness and the high rate of human mobility around the world. Although travel/movement restrictions and other non-pharmaceutical interventions aimed at controlling the disease spread were put in place during the early stages of the pandemic, these interventions did not stop COVID-19 spread. To better understand the impact of human mobility on the spread of COVID-19 between regions, we propose a hybrid gravity-metapopulation model of COVID-19. Our modeling framework has the flexibility of determining mobility between regions based on the distances between the regions or using data from mobile devices. In addition, our model explicitly incorporates time-dependent human mobility into the disease transmission rate, and has the potential to incorporate other factors that affect disease transmission such as facemasks, physical distancing, contact rates, etc. An important feature of this modeling framework is its ability to independently assess the contribution of each factor to disease transmission. Using a Bayesian hierarchical modeling framework, we calibrate our model to the weekly reported cases of COVID-19 in thirteen local health areas in Metro Vancouver, British Columbia (BC), Canada, from July 2020 to January 2021. We consider two main scenarios in our model calibration: using a fixed distance matrix and time-dependent weekly mobility matrices. We found that the distance matrix provides a better fit to the data, whilst the mobility matrices have the ability to explain the variance in transmission between regions. This result shows that the mobility data provides more information in terms of disease transmission than the distances between the regions.

Mathematical modeling and investigation on the role of demography and contact patterns in social distancing measures effectiveness in COVID-19 dissemination

In this article, we investigate the importance of demography and contact patterns in determining the spread of COVID-19 and to the effectiveness of social distancing policies. We investigate these questions proposing an augmented epidemiological model with an age-structured model, with the population divided into susceptible (S), exposed (E), asymptomatic infectious (A), hospitalized (H), symptomatic infectious (I) and recovered individuals (R), to simulate COVID-19 dissemination. The simulations were carried out using six combinations of four types of isolation policies (work restrictions, isolation of the elderly, community distancing and school closures) and four representative fictitious countries generated over alternative demographic transition stage patterns (aged developed, developed, developing and least developed countries). We concluded that the basic reproduction number depends on the age profile and the contact patterns. The aged developed country had the lowest basic reproduction number ($R0=1.74$) due to the low contact rate among individuals, followed by the least developed country ($R0=2.00$), the developing country ($R0=2.43$) and the developed country ($R0=2.64$). Because of these differences in the basic reproduction numbers, the same intervention policies had higher efficiencies in the aged and least developed countries. Of all intervention policies, the reduction in work contacts and community distancing were the ones that produced the highest decrease in the $R0$ value, prevalence, maximum hospitalization demand and fatality rate. The isolation of the elderly was more effective in the developed and aged developed countries. The school closure was the less effective intervention policy, though its effects were not negligible in the least developed and developing countries.

A Strategy Formulation Framework for Efficient Screening during the Early Stage of a Pandemic

For viruses that can be transmitted by contacts of people, efficiently screening infected individuals is beneficial for controlling outbreaks rapidly and avoiding widespread diffusion, especially during the early stage of a pandemic. The process of virus transmission can be described as virus diffusion in complex networks such as trajectory networks. We propose a strategy formulation framework (SFF) for generating various screening strategies to identify influential nodes in networks. We propose two types of metrics to measure the nodes' influence and three types of screening modes. Then, we can obtain six combinations, i.e., six strategies. To verify the efficiencies of the strategies, we build a scenario model based on the multi-agent modelling. In this model, people can move according to their self-decisions, and a virtual trajectory network is generated by their contacts. We found that (1) screening people will have a better performance based on their contact paths if there is no confirmed case yet, and (2) if the first confirmed case has been discovered, it is better to screen people sequentially by their influences. The proposed SFF and strategies can provide support for decision makers, and the proposed scenario model can be applied to simulate and forecast the virus-diffusion process.

A generalized distributed delay model of COVID-19: An endemic model with immunity waning

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been spreading worldwide for over two years, with millions of reported cases and deaths. The deployment of mathematical modeling in the fight against COVID-19 has recorded tremendous success. However, most of these models target the epidemic phase of the disease. The development of safe and effective vaccines against SARS-CoV-2 brought hope of safe reopening of schools and businesses and return to pre-COVID normalcy, until mutant strains like the Delta and Omicron variants, which are more infectious, emerged. A few months into the pandemic, reports of the possibility of both vaccine- and infection-induced immunity waning emerged, thereby indicating that COVID-19 may be with us for longer than earlier thought. As a result, to better understand the dynamics of COVID-19, it is essential to study the disease with an endemic model. In this regard, we developed and analyzed an endemic model of COVID-19 that incorporates the waning of both vaccine- and infection-induced immunities using distributed delay equations. Our modeling framework assumes that the waning of both immunities occurs gradually over time at the population level. We derived a nonlinear ODE system from the distributed delay model and showed that the model could exhibit either a forward or backward bifurcation depending on the immunity waning rates. Having a backward bifurcation implies that $ R_c < 1 $ is not sufficient to guarantee disease eradication, and that the immunity waning rates are critical factors in eradicating COVID-19. Our numerical simulations show that vaccinating a high percentage of the population with a safe and moderately effective vaccine could help in eradicating COVID-19.

Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections

The world experienced the life-threatening COVID-19 disease worldwide since its inversion. The whole world experienced difficult moments during the COVID-19 period, whereby most individual lives were affected by the disease socially and economically. The disease caused millions of illnesses and hundreds of thousands of deaths worldwide. To fight and control the COVID-19 disease intensity, mathematical modeling was an essential tool used to determine the potentiality and seriousness of the disease. Due to the effects of the COVID-19 disease, scientists observed that vaccination was the main option to fight against the disease for the betterment of human lives and the world economy. Unvaccinated individuals are more stressed with the disease, hence their body's immune system are affected by the disease. In this study, the S V E I H R deterministic model of COVID-19 with six compartments was proposed and analyzed. Analytically, the next-generation matrix method was used to determine the basic reproduction number ( R 0 ). Detailed stability analysis of the no-disease equilibrium ( E 0 ) of the proposed model to observe the dynamics of the system was carried out and the results showed that E 0 is stable if R 0 < 1 and unstable when R 0 > 1 . The Bayesian Markov Chain Monte Carlo (MCMC) method for the parameter identifiability was discussed. Moreover, the sensitivity analysis of R 0 showed that vaccination was an essential method to control the disease. With the presence of a vaccine in our S V E I H R model, the results showed that R 0 = 0 . 208 , which means COVID-19 is fading out of the community and hence minimizes the transmission. Moreover, in the absence of a vaccine in our model, R 0 = 1 . 7214 , which means the disease is in the community and spread very fast. The numerical simulations demonstrated the importance of the proposed model because the numerical results agree with the sensitivity results of the system. The numerical simulations also focused on preventing the disease to spread in the community.

Association between close interpersonal contact and vaccine hesitancy: Findings from a population-based survey in Canada

Background

Vaccine hesitancy threatens efforts to bring the coronavirus disease 2019 (COVID-19) pandemic to an end. Given that social or interpersonal contact is an important driver for COVID-19 transmission, understanding the relationship between contact rates and vaccine hesitancy may help identify appropriate targets for strategic intervention. The purpose of this study was to assess the association between interpersonal contact and COVID-19 vaccine hesitancy among a sample of unvaccinated adults in the Canadian province of British Columbia (BC).

Methods

Unvaccinated individuals participating in the BC COVID-19 Population Mixing Patterns Survey (BC-Mix) were asked to indicate their level of agreement to the statement, "I plan to get the COVID-19 vaccine." Multivariable multinomial logistic regression was used to assess the association between self-reported interpersonal contact and vaccine hesitancy, adjusting for age, sex, ethnicity, educational attainment, occupation, household size and region of residence. All analyses incorporated survey sampling weights based on age, sex, geography, and ethnicity.

Results

Results were based on survey responses collected between March 8, 2021 and December 6, 2021, by a total of 4,515 adults aged 18 years and older. Overall, 56.7% of respondents reported that they were willing to get the COVID-19 vaccine, 27.0% were unwilling and 16.3% were undecided. We found a dose-response association between interpersonal contact and vaccine hesitancy. Compared to individuals in the lowest quartile (least contact), those in the fourth quartile (highest contact), third quartile and second quartile groups were more likely to be vaccine hesitant, with adjusted odd ratios (aORs) of 2.85 (95% CI: 2.02, 4.00), 1.91(95% CI: 1.38, 2.64), 1.78 (95% CI: 1.13, 2.82), respectively.

Conclusion

Study findings show that among unvaccinated people in BC, vaccine hesitancy is greater among those who have high contact rates, and hence potentially at higher risk of acquiring and transmitting infection. This may also impact future uptake of booster doses.

The heterogeneous mixing model of COVID-19 with interventions

The emergence of mutant strains of COVID-19 reduces the effectiveness of vaccines in preventing infection, but remains effective in preventing severe illness and death. This paper established a heterogeneous mixing model of age groups with pharmaceutical and non-pharmaceutical interventions by analyzing the transmission mechanism of breakthrough infection caused by the heterogeneity of protection period under the action of vaccine-preventable infection with the original strain. The control reproduction number Rc of the system is analyzed, and the existence and stability of equilibrium are given by the comparison principle. Numerical simulation was conducted to evaluate the vaccination program and intervention measures in the customized scenario, demonstrating that the group-3 coverage rate p3 plays a key role in Rc. It is proposed that accelerating the rate of admission and testing is conducive to epidemic control by further fitting data of COVID-19 transmission in real scenarios. The findings provide a general modeling idea for the emergence of new vaccines to prevent infection by mutant strains, as well as a solid theoretical foundation for mainland China to formulate future vaccination strategies for new vaccines. This manuscript was submitted as part of a theme issue on “Modelling COVID-19 and Preparedness for Future Pandemics”.

Cohort profile: the British Columbia COVID-19 Population Mixing Patterns Survey (BC-Mix)

PURPOSE

Several non-pharmaceutical interventions, such as physical distancing, handwashing, self-isolation, and school and business closures, were implemented in British Columbia (BC) following the first laboratory-confirmed case of COVID-19 on 26 January 2020, to minimise in-person contacts that could spread infections. The BC COVID-19 Population Mixing Patterns Survey (BC-Mix) was established as a surveillance system to measure behaviour and contact patterns in BC over time to inform the timing of the easing/re-imposition of control measures. In this paper, we describe the BC-Mix survey design and the demographic characteristics of respondents.

PARTICIPANTS

The ongoing repeated online survey was launched in September 2020. Participants are mainly recruited through social media platforms (including Instagram, Facebook, YouTube, WhatsApp). A follow-up survey is sent to participants 2-4 weeks after completing the baseline survey. Survey responses are weighted to BC's population by age, sex, geography and ethnicity to obtain generalisable estimates. Additional indices such as the Material and Social Deprivation Index, residential instability, economic dependency, and others are generated using census and location data.

FINDINGS TO DATE

As of 26 July 2021, over 61 000 baseline survey responses were received of which 41 375 were eligible for analysis. Of the eligible participants, about 60% consented to follow-up and about 27% provided their personal health numbers for linkage with healthcare databases. Approximately 83.5% of respondents were female, 58.7% were 55 years or older, 87.5% identified as white and 45.9% had at least a university degree. After weighting, approximately 50% were female, 39% were 55 years or older, 65% identified as white and 50% had at least a university degree.

FUTURE PLANS

Multiple papers describing contact patterns, physical distancing measures, regular handwashing and facemask wearing, modelling looking at impact of physical distancing measures and vaccine acceptance, hesitancy and uptake are either in progress or have been published.