Novel approach for modeling spread of infectious disease

By Dr. Ananya Mandal, MDNov 4 2020

Nearly 48 million people worldwide have been infected with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) that causes COVID-19 disease. The virus spreads rapidly from person to person, and since its emergence in late December 2019, the dynamics of its spread has been studied extensively.

Researchers M. Shayak from the Department of Theoretical and Applied Mechanics, Mechanical and Aerospace Engg, Cornell University, New York State, and Mohit Sharma from the Department of Population Health Sciences, Weill Cornell Medicine, New York State, USA, delved into the dynamics of the spread of infectious diseases in the context of the current pandemic. Their study titled, "A New Approach to the Dynamic Modeling of an Infectious Disease," was released pre-publication on the medRxiv* server.

Study: A New Approach to the Dynamic Modeling of an Infectious Disease. Image Credit: Kateryna Kon / Shutterstock

This news article was a review of a preliminary scientific report that had not undergone peer-review at the time of publication. Since its initial publication, the scientific report has now been peer reviewed and accepted for publication in a Scientific Journal. Links to the preliminary and peer-reviewed reports are available in the Sources section at the bottom of this article. View Sources

Background and purpose of research

The rapid spread of SARS-CoV-2 across the world despite the early shutdown of borders and the cessation of international travel has sparked interest and given rise to changes in knowledge regarding the spread of infections. The research duo feels that mathematical modeling remains the "only scientific tool that allows us to predict the disease's trajectories in advance and take intervention measures accordingly."

According to the researchers, there are four approaches for such modeling. These include:

• Lumped parameter or compartmental model used over a century earlier to model the spread dynamics of plague - this study used this model.
• Agent-based model - considers the individuals in a population as "lattice sites on a network." Used by the London School of Hygiene and Tropical Medicine, Imperial College, and Los Alamos National Laboratory.
• Stochastic differential equation model – combines the features of both the above methods. Examples include the Cornell University model and the Jadavpur University model.
• Data-driven model – Takes the existing data on the spread of COVID-19 over the past week or month and uses machine learning to generate a prediction or forecast of spread.

The baseline mode

In the baseline model, the researchers present the derivation and solutions of the baseline model. The team assumes permanent immunity i.e., all recovered cases are insusceptible to further infection for all time. The population of cases divided into three parts.

• contact traced cases
• untraced symptomatic cases
• untraced asymptomatic cases

This study showed that the baseline model itself was capable of generating a diverse range of epidemic trajectories. These match the course of the pandemic seen around the world in real-time, they wrote. They call this baseline model "realistic" and advantageous when compared to conventional lumped parameter models. The team wrote, "Henceforth, we focus on the extension of the baseline model to various scenarios which can and do arise in reality, in terms of both public health interventions and immune response."

Public health effects

The team declares that as private researchers, they did not have access to all public health data but attempt to use the available data to predict disease spread trajectories and effects on population health. They gathered data such as numbers of hospitalizations and deaths as well as cumulative cases.

Some of the variables they took into account were the age and vulnerability of the populations and the structure of the transmission of the infection. They classified society into two classes – young people and older people. Young were those who were least vulnerable, irrespective of age. This included even immunocompetent 60-year olds with no known comorbidities. Old were those who were vulnerable, even including 20-year olds with known immune disorders.

Their calculations showed, "Not only is the unmasked population infected almost entirely, but also there is more than 50 percent infection level among the masked people." They added, "This type of statistic can be used by public health authorities to encourage mask use – by not masking, not only are you increasing your own chances of catching corona but you are subjecting the law-abiding people to extra risk as well."

They also found superspreaders to be of two types:

• people who interact with others a lot
• people who have exceptionally high viral loads and infect almost whomever they come into contact with

Effects of immunity

The researchers assumed that prior infection would provide permanent immunity and prevent further infections.

The team considered the case where immunity against the disease lasts for a fixed, limited duration first. They predicted a trajectory of the infections and their recoveries in this scenario.

In case of a complex immune response to the infection. They assumed three different immune responses, "sterilizing immunity which completely prevents reinfection, severity-reducing immunity which mitigates the symptoms during reinfection and transmissibility-reducing immunity which mitigates the patient's transmissibility during reinfection." They also take into consideration a severe form, "antibody-dependent enhancement (ADE) in which case a reinfection takes a more severe form than the original infection."

Using these scenarios, the team predicted trajectories of the infection in the populations.

Conclusions and implications for future

Using the mathematical models, the team says that it is possible to create models that combine different variations including mask use, contact tracing, and complex immune responses to the infection.

Authors conclude, "Infectious disease has always been a part of human existence, and with the advent of jetliner travel, pathogens can be carried halfway across the world in a matter of hours. With current trends continuing, it is highly probable that pandemics are here to stay. We hope that the same may be said of our model as well."

This news article was a review of a preliminary scientific report that had not undergone peer-review at the time of publication. Since its initial publication, the scientific report has now been peer reviewed and accepted for publication in a Scientific Journal. Links to the preliminary and peer-reviewed reports are available in the Sources section at the bottom of this article. View Sources