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Optimality of a time-dependent treatment profile during an epidemic.

Jaberi-Douraki M, Moghadas SM - J Biol Dyn (2013)

Bottom Line: The emergence and spread of drug resistance is one of the most challenging public health issues in the treatment of some infectious diseases.The objective of this work is to investigate whether the effect of resistance can be contained through a time-dependent treatment strategy during the epidemic subject to an isoperimetric constraint.We demonstrate that both the rate of resistance emergence and the relative transmissibility of the resistant strain play important roles in determining the optimal timing and level of treatment profile.

View Article: PubMed Central - PubMed

Affiliation: Agent-Based Modelling Laboratory, York University, Toronto, Ontario M3J 1P3, Canada. majid.jaberi-douraki@mail.mcgill.ca

ABSTRACT
The emergence and spread of drug resistance is one of the most challenging public health issues in the treatment of some infectious diseases. The objective of this work is to investigate whether the effect of resistance can be contained through a time-dependent treatment strategy during the epidemic subject to an isoperimetric constraint. We apply control theory to a population dynamical model of influenza infection with drug-sensitive and drug-resistant strains, and solve the associated control problem to find the optimal treatment profile that minimizes the cumulative number of infections (i.e. the epidemic final size). We consider the problem under the assumption of limited drug stockpile and show that as the size of stockpile increases, a longer delay in start of treatment is required to minimize the total number of infections. Our findings show that the amount of drugs used to minimize the total number of infections depends on the rate of de novo resistance regardless of the initial size of drug stockpile. We demonstrate that both the rate of resistance emergence and the relative transmissibility of the resistant strain play important roles in determining the optimal timing and level of treatment profile.

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Model diagram for the transitions between sub-populations with emergence of resistance during treatment.
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Figure 1: Model diagram for the transitions between sub-populations with emergence of resistance during treatment.

Mentions: We consider a deterministic model of influenza epidemic [28] that describes the transmission dynamics of drug-sensitive and drug-resistant strains in a host population. The compartmental model divides a randomly mixed population into classes of individuals who are susceptible to infection (S); infected with the sensitive strain (IU); treated (IT); and infected with the drug-resistant strain (IR). Since treatment is effective only against drug-sensitive infection, we combined treated and untreated classes of individuals infected with the drug-resistant strain. The transitions between these classes are represented in Figure 1, and mathematically formulated by the following system of differential equations:


Optimality of a time-dependent treatment profile during an epidemic.

Jaberi-Douraki M, Moghadas SM - J Biol Dyn (2013)

Model diagram for the transitions between sub-populations with emergence of resistance during treatment.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3753656&req=5

Figure 1: Model diagram for the transitions between sub-populations with emergence of resistance during treatment.
Mentions: We consider a deterministic model of influenza epidemic [28] that describes the transmission dynamics of drug-sensitive and drug-resistant strains in a host population. The compartmental model divides a randomly mixed population into classes of individuals who are susceptible to infection (S); infected with the sensitive strain (IU); treated (IT); and infected with the drug-resistant strain (IR). Since treatment is effective only against drug-sensitive infection, we combined treated and untreated classes of individuals infected with the drug-resistant strain. The transitions between these classes are represented in Figure 1, and mathematically formulated by the following system of differential equations:

Bottom Line: The emergence and spread of drug resistance is one of the most challenging public health issues in the treatment of some infectious diseases.The objective of this work is to investigate whether the effect of resistance can be contained through a time-dependent treatment strategy during the epidemic subject to an isoperimetric constraint.We demonstrate that both the rate of resistance emergence and the relative transmissibility of the resistant strain play important roles in determining the optimal timing and level of treatment profile.

View Article: PubMed Central - PubMed

Affiliation: Agent-Based Modelling Laboratory, York University, Toronto, Ontario M3J 1P3, Canada. majid.jaberi-douraki@mail.mcgill.ca

ABSTRACT
The emergence and spread of drug resistance is one of the most challenging public health issues in the treatment of some infectious diseases. The objective of this work is to investigate whether the effect of resistance can be contained through a time-dependent treatment strategy during the epidemic subject to an isoperimetric constraint. We apply control theory to a population dynamical model of influenza infection with drug-sensitive and drug-resistant strains, and solve the associated control problem to find the optimal treatment profile that minimizes the cumulative number of infections (i.e. the epidemic final size). We consider the problem under the assumption of limited drug stockpile and show that as the size of stockpile increases, a longer delay in start of treatment is required to minimize the total number of infections. Our findings show that the amount of drugs used to minimize the total number of infections depends on the rate of de novo resistance regardless of the initial size of drug stockpile. We demonstrate that both the rate of resistance emergence and the relative transmissibility of the resistant strain play important roles in determining the optimal timing and level of treatment profile.

Show MeSH
Related in: MedlinePlus