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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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Epidemic final size as a function of the treatment level and delay in start of treatment, with α = 10−3 and δR = 0.9, for (a) K = 5%; (b) K = 10%; (c) K = 15%; and (d) K = 20%. Other parameter values are given Table 1.
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Figure 3: Epidemic final size as a function of the treatment level and delay in start of treatment, with α = 10−3 and δR = 0.9, for (a) K = 5%; (b) K = 10%; (c) K = 15%; and (d) K = 20%. Other parameter values are given Table 1.

Mentions: To explore the effect of the size of drug stockpile on the optimal treatment profile, we simulated the model for K = 5%, 10%, 15%, 20%. Figure 3 shows the epidemic final size for different amounts of drug stockpile. Clearly, as the size of stockpile increases, a longer delay in start of treatment is required to minimize the total number of infections, which corresponds to a smaller region for optimal profile. It is, however, important to note that the amount of drugs used to minimize the total number of infections (corresponding to the optimal scenario) depends on the rate of resistance emergence regardless of the initial size of drug stockpile. Figure 4 shows the final size as a function of the drug stockpile for different values of α. As α increases, a larger drug stockpile is required to minimize the total number of infections.


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

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

Epidemic final size as a function of the treatment level and delay in start of treatment, with α = 10−3 and δR = 0.9, for (a) K = 5%; (b) K = 10%; (c) K = 15%; and (d) K = 20%. Other parameter values are given Table 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Epidemic final size as a function of the treatment level and delay in start of treatment, with α = 10−3 and δR = 0.9, for (a) K = 5%; (b) K = 10%; (c) K = 15%; and (d) K = 20%. Other parameter values are given Table 1.
Mentions: To explore the effect of the size of drug stockpile on the optimal treatment profile, we simulated the model for K = 5%, 10%, 15%, 20%. Figure 3 shows the epidemic final size for different amounts of drug stockpile. Clearly, as the size of stockpile increases, a longer delay in start of treatment is required to minimize the total number of infections, which corresponds to a smaller region for optimal profile. It is, however, important to note that the amount of drugs used to minimize the total number of infections (corresponding to the optimal scenario) depends on the rate of resistance emergence regardless of the initial size of drug stockpile. Figure 4 shows the final size as a function of the drug stockpile for different values of α. As α increases, a larger drug stockpile is required to minimize the total number of infections.

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