Optimizing Real-Time Vaccine Allocation in a Stochastic SIR Model

Abstract

Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in delayed vaccine deployment, and the interaction between members of different cities facilitates a wide spatial spread of infection. Limited vaccine, time delays, and interaction (or coupling) of cities lead to tradeoffs that impact the overall magnitude of the epidemic. These tradeoffs mandate investigation of optimal strategies that minimize the severity of the epidemic by prioritizing allocation of vaccine to specific subpopulations. We use an SIR model to describe the disease dynamics of an epidemic which breaks out in one city and spreads to another. We solve a master equation to determine the resulting probability distribution of the final epidemic size. We then identify tradeoffs between vaccine, time delay, and coupling, and we determine the optimal vaccination protocols resulting from these tradeoffs.

Computational Health Engineering Applied to Model Infectious Diseases and Antimicrobial Resistance Spread

“…The stochastic approach takes random variables into consideration. Susceptible-Infection-Recover (SIR) compartments and derivatives models are mainly used for predictions about the spread of infectious diseases [39], vaccination impact [40], or both [41,42]. Importantly, population dynamics are inexorably subjected to environmental background and natural phenomena, and rather than following random oscillations, they strictly follow deterministic laws.…”

The benefits of combining early aspecific vaccination with later specific vaccination

“…They formulate a stochastic programming problem and show how the optimal allocation depends on the minimum required levels. Nguyen and Carlson (2016) compare different vaccination strategies which differ in when and how much vaccines become available.…”

“…The latter might seem worse, but might have a lower price, a shorter delivery time or may be available in larger quantities. Nguyen and Carlson (2016) vary the time at which vaccines become available and the stockpile size to determine the effects on the epidemic.…”

Optimal vaccine allocation during the mumps outbreak in two SIR centres

“…Limited amount of vaccine and its optimal allocation were investigated for non-interacting centers in deterministic [22] and stochastic [23] cases. Interacting centers without migration in deterministic and stochastic cases were considered in [24]. The optimal vaccine allocation in different vaccination schedules in two centers was studied in [25] for the typical fixed parameters values without analyzing the dependence of the parameters domain-wide.…”

“…Interacting centers in the form of epidemic percolation network were considered in [26,27]. In [22] authors maximize the total number of people that escape infection, in papers [23,24] they minimize the final quantity of removed and infectives, in paper [25] they minimize a mortality. These functionals are interesting from a healthcare point of view.…”