Mathematical Biology

During an epidemic, the interplay of disease and opinion dynamics can lead to outcomes that are different from those predicted based on disease dynamics alone. Opinions and the behaviors they elicit are complex, so modeling them requires a measure of abstraction and simplification. In this talk, we develop a differential equation model that couples SIR-type disease dynamics with opinion dynamics. We assume a spectrum of opinions that change based on current levels of infection as well as interactions that to some extent amplify the opinions of like-minded individuals. Susceptibility to infection is based on the level of prophylaxis (disease avoidance) that an opinion engenders. In this setting, we observe how the severity of an epidemic is influenced by the distribution of opinions at disease introduction, the relative rates of opinion and disease dynamics, and the amount of opinion amplification. Some insight is gained by considering how the effective reproduction number is influenced by the combination of opinion and disease dynamics.

We present a simulation study of the spread of an epidemic like COVID-19 with temporary immunity on finite spatial and non-spatial network models. In particular, we assume that an epidemic spreads stochastically on a scale-free network and that each infected individual in the network gains a temporary immunity after its infectious period is over. After the temporary immunity period is over, the individual becomes susceptible to the virus again. When the underlying contact network is embedded in Euclidean geometry, we model three different intervention strategies that aim to control the spread of the epidemic: social distancing, restrictions on travel, and restrictions on maximal number of social contacts per node. Our first finding is that on a finite network, a long enough average immunity period leads to extinction of the pandemic after the first peak, analogous to the concept of ``herd immunity''. For each model, there is a critical average immunity duration $L_c$ above which this happens. Our second finding is that all three interventions manage to flatten the first peak (the travel restrictions most efficiently), as well as decrease the critical immunity duration $L_c$, but elongate the epidemic. However, when the average immunity duration $L$ is shorter than $L_c$, the price for the flattened first peak is often a high second peak: for limiting the maximal number of contacts, the second peak can be as high as 1/3 of the first peak, and twice as high as it would be without intervention. Thirdly, interventions introduce oscillations into the system and the time to reach equilibrium is, for almost all scenarios, much longer. We conclude that network-based epidemic models can show a variety of behaviors that are not captured by the continuous compartmental models.

Community spread of coronavirus disease 2019 (COVID-19) continues to be high in many areas, likely due, in part, to insufficient testing and contact tracing. As regional test kit shortages are likely to continue with increased transmission, it is important that available testing capacity be used effectively. To date, testing for COVID-19 has largely been restricted to persons reporting symptoms, with no additional criteria being systematically employed to select who is tested. In situations when testing capacity is limited, we propose the use of a clinical prediction rule to allow for prioritized testing of people who are most likely to test positive for COVID-19. Using data from the University of Utah Health system, we developed a robust, deployable clinical prediction rule which incorporates data on demographics and clinical characteristics to predict which patients are most likely to test positive. We then incorporated prioritized testing into a stochastic SEIR model for COVID-19 to measure changes in disease burden compared to a model with indiscriminate testing. Our best performing clinical prediction rule achieved an AUC of 0.7. When incorporated into the SEIR model, prioritized testing resulted in a delay in the timing of the infection peak, a meaningful reduction in both the total number of infected individuals and the peak height of the infection curve, and thus a reduction in the excess demand on local hospital resources. These effects were strongest for lower values of Rt and higher proportions of infected individuals seeking testing.

SARS-CoV-2 is a novel pathogen causes the COVID-19 pandemic. Some of the basic epidemiological parameters, such as the exponential epidemic growth rate and R0 are debated. We collected and analyzed data from China, eight European countries and the US using a variety of inference approaches. In all countries, the early epidemic grew exponentially at rates between 0.19-0.29/day (epidemic doubling times between 2.4-3.7 days). I will discuss the appropriate serial intervals to estimate the basic reproductive number R0 and argue that existing evidence suggests a highly infectious virus with an R0 likely between 4.0 and 7.1. Further, we found that similar levels of intervention efforts are needed, no matter the goal is mitigation or containment. Early, strong and comprehensive intervention efforts to achieve greater than 74-86% reduction in transmission are necessary.

On March 23rd and March 30th, 2020, the Mexican Federal government implemented social distancing measures to mitigate the COVID-19 epidemic. In this work a mathematical model is used to explore atypical transmission events within the confinement period, triggered by the timing and strength of short time perturbations of social distancing. Is shown that social distancing measures were successful in achieving a significant reduction of the epidemic curve growth rate in the early weeks of the intervention. However, “flattening the curve” had an undesirable effect, since the epidemic peak was delayed too far, almost to the government preset day for lifting restrictions (June 1st, 2020). If the peak indeed occurs in late May or early June, then the events of children's day and Mother’s Day may either generate a later peak (worst case scenario), a long plateau with relatively constant but high incidence (middle case scenario) or the same peak date as in the original baseline epidemic curve, but with a post-peak interval of slower decay.