Can treatment increase the epidemic size?
type: Item
instance of: scholarly article
title: Can treatment increase the epidemic size?
zbMATH Open document ID: 1353.92106
author: Yanyu Xiao
author: Fred Brauer
author: Seyed M. Moghadas
published in: Journal of Mathematical Biology
publication date: 2016-02-02T00:00:00Z
review text: This paper studies an epidemic model with drug-sensitive and drug-resistant pathogen strains over a constant homogeneously mixed population. The model can be expressed in the form \[ \begin{aligned} S'&=-\beta(I_S+\delta_TI_T+\delta_RI_R)S, \\ I'_S&=\beta(I_S+\delta_TI_T)S-(\gamma_S+\eta)I_S,\\ I'_T&=\eta I_S+\int_0^t\eta I_S(\xi)e^{-\gamma_T(t-\xi)}\alpha'(t-\xi)d\xi-\gamma_TI_T,\\ I'_R&=\delta_R\beta I_RS-\int_0^t\eta I_S(\xi)e^{-\gamma_T(t-\xi)}\alpha'(t-\xi)d\xi-\gamma_RI_R,\end{aligned} \] where the status is classified as susceptible (\(S\)), infected with the sensitive strain (\(I_S\)), with the sensitive strain under treatment (\(I_T\)), and with the resistant strain (\(I_R\)). Here, \(\beta\) is the baseline transmission rate; \(\delta_R,\delta_T\), and \(\eta\) are the relative transmissibility of the resistant strain, treated infection with the sensitive strain, and the rate at which individuals infected with the sensitive strain are treated, respectively; \(\gamma_S,\gamma_T,\gamma_R\) are the corresponding recovery rates. \(\alpha(t)\) is a non-negative non-increasing function representing the probability of being in the treated class (\(I_T\)) at time \(t\) following the initiation of treatment without developing drug-resistance. Under some ad hoc assumptions on these parameters and functions, the authors obtain the final epidemic size relations with respect to the treatment rate for the model, giving an affirmative answer to the title. Numerical results are presented to illustrate the theoretical findings.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 6538264
zbMATH Keywords: epidemic modelling
zbMATH Keywords: treatment
zbMATH Keywords: drug-resistance
zbMATH Keywords: reproduction number
Wikidata QID: Q40997093
MaRDI profile type: Publication
full work available at URL: s00285-015-0887-y
OpenAlex ID: W1973049848
cites work: Mathematical Models in Population Biology and Epidemiology
cites work: Q4255467
cites work: Q5425001
cites work: Resistance to larvicides in mosquito populations and how it could benefit malaria control
cites work: Emergence of Resistance in Influenza With Compensatory Mutations
cites work: Modeling relapse in infectious diseases
cites work: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
cites work: On latencies in malaria infections and their impact on the disease dynamics
DOI: 10.1007/S00285-015-0887-Y
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description: scientific article; zbMATH DE number 6538264