Mathematical modeling of mpox: A scoping review

Background

Mpox (monkeypox), a disease historically endemic to Africa, has seen its largest outbreak in 2022 by spreading to many regions of the world and has become a public health threat. Informed policies aimed at controlling and managing the spread of this disease necessitate the use of adequate mathematical modeling strategies.

Objective

In this scoping review, we sought to identify the mathematical models that have been used to study mpox transmission in the literature in order to determine what are the model classes most frequently used, their assumptions, and the modelling gaps that need to be addressed in the context of the epidemiological characteristics of the ongoing mpox outbreak.

Methods

This study employed the methodology of the PRISMA guidelines for scoping reviews to identify the mathematical models available to study mpox transmission dynamics. Three databases (PubMed, Web of Science and MathSciNet) were systematically searched to identify relevant studies.

Results

A total of 5827 papers were screened from the database queries. After the screening, 35 studies that met the inclusion criteria were analyzed, and 19 were finally included in the scoping review. Our results show that compartmental, branching process, Monte Carlo (stochastic), agent-based, and network models have been used to study mpox transmission dynamics between humans as well as between humans and animals. Furthermore, compartmental and branching models have been the most commonly used classes.

Conclusions

There is a need to develop modeling strategies for mpox transmission that take into account the conditions of the current outbreak, which has been largely driven by human-to-human transmission in urban settings. In the current scenario, the assumptions and parameters used by most of the studies included in this review (which are largely based on a limited number of studies carried out in Africa in the early 80s) may not be applicable, and therefore, can complicate any public health policies that are derived from their estimates. The current mpox outbreak is also an example of how more research into neglected zoonoses is needed in an era where new and re-emerging diseases have become global public health threats.

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.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-022-13597-9.

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.

School and community reopening during the COVID-19 pandemic: a mathematical modelling study

Operating schools safely during the COVID-19 pandemic requires a balance between health risks and the need for in-person learning. Using demographic and epidemiological data between 31 July and 23 November 2020 from Toronto, Canada, we developed a compartmental transmission model with age, household and setting structure to study the impact of schools reopening in September 2020. The model simulates transmission in the home, community and schools, accounting for differences in infectiousness between adults and children, and accounting for work-from-home and virtual learning. While we found a slight increase in infections among adults (2.2%) and children (4.5%) within the first eight weeks of school reopening, transmission in schools was not the key driver of the virus resurgence in autumn 2020. Rather, it was community spread that determined the outbreak trajectory, primarily due to increases in contact rates among adults in the community after school reopening. Analyses of cross-infection among households, communities and schools revealed that home transmission is crucial for epidemic progression and safely operating schools, while the degree of in-person attendance has a larger impact than other control measures in schools. This study suggests that safe school reopening requires the strict maintenance of public health measures in the community.

Quantifying the annual incidence and underestimation of seasonal influenza: A modelling approach

BACKGROUND

Seasonal influenza poses a significant public health and economic burden, associated with the outcome of infection and resulting complications. The true burden of the disease is difficult to capture due to the wide range of presentation, from asymptomatic cases to non-respiratory complications such as cardiovascular events, and its seasonal variability. An understanding of the magnitude of the true annual incidence of influenza is important to support prevention and control policy development and to evaluate the impact of preventative measures such as vaccination.

METHODS

We use a dynamic disease transmission model, laboratory-confirmed influenza surveillance data, and randomized-controlled trial (RCT) data to quantify the underestimation factor, expansion factor, and symptomatic influenza illnesses in the US and Canada during the 2011-2012 and 2012-2013 influenza seasons.

RESULTS

Based on 2 case definitions, we estimate between 0.42-3.2% and 0.33-1.2% of symptomatic influenza illnesses were laboratory-confirmed in Canada during the 2011-2012 and 2012-2013 seasons, respectively. In the US, we estimate between 0.08-0.61% and 0.07-0.33% of symptomatic influenza illnesses were laboratory-confirmed in the 2011-2012 and 2012-2013 seasons, respectively. We estimated the symptomatic influenza illnesses in Canada to be 0.32-2.4 million in 2011-2012 and 1.8-8.2 million in 2012-2013. In the US, we estimate the number of symptomatic influenza illnesses to be 4.4-34 million in 2011-2012 and 23-102 million in 2012-2013.

CONCLUSIONS

We illustrate that monitoring a representative group within a population may aid in effectively modelling the transmission of infectious diseases such as influenza. In particular, the utilization of RCTs in models may enhance the accuracy of epidemiological parameter estimation.