Age-stratified transmission model of COVID-19 in Ontario with human mobility during pandemic's first wave.

In this work, we employ a data-fitted compartmental model to visualize the progression and behavioral response to COVID-19 that match provincial case data in Ontario, Canada from February to June of 2020. This is a "rear-view mirror" glance at how this region has responded to the 1st wave of the pandemic, when testing was sparse and NPI measures were the only remedy to stave off the pandemic. We use an SEIR-type model with age-stratified subpopulations and their corresponding contact rates and asymptomatic rates in order to incorporate heterogeneity in our population and to calibrate the time-dependent reduction of Ontario-specific contact rates to reflect intervention measures in the province throughout lockdown and various stages of social-distancing measures. Cellphone mobility data taken from Google, combining several mobility categories, allows us to investigate the effects of mobility reduction and other NPI measures on the evolution of the pandemic. Of interest here is our quantification of the effectiveness of Ontario's response to COVID-19 before and after provincial measures and our conclusion that the sharp decrease in mobility has had a pronounced effect in the first few weeks of the lockdown, while its effect is harder to infer once other NPI measures took hold.

Adoption costs of new vaccines - A Stackelberg dynamic game with risk-perception transition states.

Vaccination has become an integral part of public health, since an increase in overall vaccination in a given population contributes to a decline in infectious diseases and mortality. Vaccination also contributes to a lower rate of infection even for nonvaccinators due to herd immunity ((Brisson and Edmunds, 2002)). In this work we model human decision-making (with respect to a vaccination program in a single-payer health care provider country) using a leader-follower game framework. We then extend our model to a discrete dynamic game, where time passing is modelled by risk perception changes among population groups considering whether or not to vaccinate. The risk perception changes are encapsulated by probability transition matrices. We assume that the single-payer provider has a given fixed budget which would not be sufficient to cover 100% of a new vaccine for the entire population. To increase the potential coverage, we propose the introduction of a partial vaccine adoption policy, whereby an individual would pay a portion of the vaccine price and the single payer would support the rest for the entire population. We show how this policy, together with changes in risk perceptions regarding vaccination, impact the strategic decisions of individuals in each group, the policy cost under budgetary constraints and, ultimately, how it impacts the overall uptake of the vaccine in the entire population.

Examining Ontario's universal influenza immunization program with a multi-strain dynamic model.

Seasonal influenza imposes a significant worldwide health burden each year. Mathematical models help us to understand how changes in vaccination affect this burden. Here, we develop a new dynamic transmission model which directly tracks the four dominant seasonal influenza strains/lineages, and use it to retrospectively examine the impact of the switch from a targeted to a universal influenza immunization program (UIIP) in the Canadian province of Ontario in 2000. According to our model results, averaged over the first four seasons post-UIIP, the rates of influenza-associated health outcomes in Ontario were reduced to about half of their pre-UIIP values. This is conservative compared to the results of a study estimating the UIIP impact from administrative data, though that study finds age-specific trends similar to those presented here. The strain interaction in our model, together with its flexible parameter calibration scheme, make it readily extensible to studying scenarios beyond the one explored here.

The formation of Uranus and Neptune in the Jupiter-Saturn region of the Solar System.

Planets are believed to have formed through the accumulation of a large number of small bodies. In the case of the gas-giant planets Jupiter and Saturn, they accreted a significant amount of gas directly from the protosolar nebula after accumulating solid cores of about 5-15 Earth masses. Such models, however, have been unable to produce the smaller ice giants Uranus and Neptune at their present locations, because in that region of the Solar System the small planetary bodies will have been more widely spaced, and less tightly bound gravitationally to the Sun. When applied to the current Jupiter-Saturn zone, a recent theory predicts that, in addition to the solid cores of Jupiter and Saturn, two or three other solid bodies of comparable mass are likely to have formed. Here we report the results of model calculations that demonstrate that such cores will have been gravitationally scattered outwards as Jupiter, and perhaps Saturn, accreted nebular gas. The orbits of these cores then evolve into orbits that resemble those of Uranus and Neptune, as a result of gravitational interactions with the small bodies in the outer disk of the protosolar nebula.