Optimal Vaccination Campaigns Using Stochastic SIR Model and Multiobjective Impulsive Control

Abstract

A multiobjective impulsive control scheme is proposed to give answers on how optimal vaccination campaigns should be implemented, regarding two conflicting targets: making the total number of infecteds small and the vaccination campaign as handy as possible. In this paper, a stochastic SIR model is used to better depict the characteristics of a disease in practical terms, where little influences may lead to sudden and unpredictable changes in the behavior of transmissions. This model is extended to analyze the effects of impulsive vaccinations in two phases: the transient regime control, taking into account the necessity to reduce the number of infected individuals to an acceptable level in a finite time, and the permanent regime control, that will act with fixed vaccinations to avoid another outbreak. A parallel version of NSGA-II is used as the multiobjective optimization machinery, considering both the probability of eradication and the vaccination campaign costs. The final result using the proposed framework nondominated policies that can guide for public managers to decide which is the best procedure to be taken depending on the present situation.

A Synthesis of Pulsed Influenza Vaccination Policies Using an Efficient Controlled Elitism Non-Dominated Sorting Genetic Algorithm (CENSGA)

“…In determining the fitness equation, it is necessary to combine the objectives and constraints to obtain a set of feasible chromosome instances. Essentially, the goal here is minimizing the volume of infected population over time and, at the same time, to obtain a campaign that offers an effective cost within the vaccination policies [3,6].…”

“…With the introduction of vaccinations for different diseases starting from the nineteenth century, this remarkable era of vaccination has had a promising influence on public health and population growth [2]. Since then, a succession of well-planned campaigns have been documented, for instance, to reduce or eradicate hepatitis, yellow fever, polio and measles [3]. Although vaccination against contagious diseases is currently considered as an intuitive strategy to control an outbreak or epidemic, policymakers are still facing a big challenge in allocating vaccine doses to the public, especially for mutant diseases or pandemics, when the aim is eradicating the disease, or keeping it within a tolerable level with minimal cost [4].…”

A Multi-Objective Simulated Annealing Local Search Algorithm in Memetic CENSGA: Application to Vaccination Allocation for Influenza

“…The significance of the impact of vaccination on public health and the economy is widely recognized [1]. Starting in the nineteenth century, there have been numerous successful vaccination campaigns for many vaccine-preventable diseases [2]. Nowadays, vaccination against disease is a fundamental tool for controlling epidemics among populations when a licensed vaccine formula is available.…”

“…Currently, multi-objective optimization is trending as a research topic in the scientific community. This is connected to the multidimensional, discontinuous, nonconvex, and difficult-to-evaluate nature of real-world problems, especially in control problems [2]. Unlike single-objective optimization, where there is a unique optimum solution, multiobjective algorithms produce multiple solutions, collectively called nondominated points, which belong to a Pareto front.…”

“…Recently, multi-objective metaheuristic and evolutionary algorithms have dominated the field of multi-objective optimization [11], particularly simulated annealing (SA) and other heuristic algorithms. This is attributed to several factors: (1) the ability to obtain multiple solutions in a single run; (2) derivatives free (for instance, gradient-based algorithms need information about the derivative of the error concerning each potential move to minimize the mean squared error, and it would be helpful especially when the global minimum is well defined; alternatively, simulated annealing does not rely on knowledge of the derivative, as its mechanism cannot be misled by local minima attraction [12]);…”