Control Policy Mix in Measles Transmission Dynamics Using Vaccination, Therapy, and Treatment

Abstract

This paper considers a deterministic model for the dynamics of measles transmission in a population divided into six classes with respect to the disease states: susceptible, vaccinated, exposed, infected, treated, and recovered. First, we investigate the dynamical properties of the SVEITR model such as its equilibrium points, their stability, and parameter sensitivity by applying constant controls. Criteria for determining the stability of disease-free and endemic equilibrium points are provided in terms of basic reproduction number. The model is then extended by incorporating vaccination, therapy, and treatment rates as time-dependent control variables representing the level of coverages. Application of Pontryagin’s maximum principle provides the necessary conditions that must be satisfied for the existence of optimal controls aiming at minimization of the number of exposed and infected individuals simultaneously with the control effort. Numerical simulations that were carried out using the backward sweep method and Runge–Kutta scheme suggest that optimal controls under moderate and high scenarios can effectively reduce the cases of measles. In particular, the moderate scenario that utilizes the existing coverage level of 86% for MCV1 and 69% for MCV2 can degrade the cost functional by 47% of the low scenario. Meanwhile, high scenario that takes the 2020 target of 96% as coverage only makes a slight difference in reducing the number of exposed and infected individuals.

Modeling measles transmission in adults and children: Implications to vaccination for eradication

“…However, as discussed above, adult vaccination should not be overlooked as it may have a critical role in disease eradication. Our result is consistent with the previous studies ( Dipo & Dinda, 2019 ; Garba et al., 2017 ; Jaharuddin, 2020 ; Lessler et al., 2016 ; Pokharel et al., 2022 ).…”

Analysis of the different interventions scenario for programmatic measles control in Bangladesh: A modelling study

“…The second dose vaccine was introduced in 2012, and its coverage increased from 35% in 2013 to 93% in 2016 [ 25 ]. In Bangladesh, treatment coverage for asymptomatic and symptomatic measles patients are around 8% and 14%, respectively [ 26 ]. Therefore, it is essential to increases the treatment rate for both asymptomatic and symptomatic measles patients in Bangladesh.…”

“…Therefore, no ethical approval is required. 1 70 per year [24] β Transmission rate 6.99×10 −7 Fitted η First dose of vaccination rate 0.94 [25] ρ Progression rate from S to V 1 0.6 [2] σ Second dose of vaccination rate 0.93 [25] ω Recovery rate due to the second dose of vaccine 0.8 [2] α Progression rate from E to I 0.019 Fitted δ Measles related death rate 0.125 [2] γ Natural recovery rate 0.6 [2] κ Treatment rate for exposed population 0.08 [26] τ Treatment rate for infected population 0.14 [26] https://doi.org/10.1371/journal.pone.0283082.t001…”

Untitled

“…The simulation of the taken into consideration version is depicted inside the figures in this phase by using parameter's values from [148] are are ε = 0.250, ρ = 0.950, α = 0.1, γ 1 = 0.15, γ 2 = 0.1, γ 3 = 0.08, γ 4 = 0.05, ω = 0.0069, µ = 0.678, 0.885, δ I = 0.04762, δ T = 0.136, β = 0.03739, 0.575, ν I = 0.913, and ν T = 0.978. Those simulations demonstrate how variations in value have an effect at the model's behavior.…”