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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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Contour plots for the ratio Fop/Foc for α in the range (a) 10−3 − 10−1 and (b) 10−6 − 10−3. Contour plots for the ratio Kop/Koc for α in the range (c) 10−3 − 10−1 and (d) 10−6 − 10−3. Other parameter values are given in Table 1.
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Figure 6: Contour plots for the ratio Fop/Foc for α in the range (a) 10−3 − 10−1 and (b) 10−6 − 10−3. Contour plots for the ratio Kop/Koc for α in the range (c) 10−3 − 10−1 and (d) 10−6 − 10−3. Other parameter values are given in Table 1.

Mentions: To compare the outcomes of optimal scenarios in the two treatment profiles simulated in Figure 5, we defined Fop and Foc to be the final sizes of the epidemic in the time-dependent and constant treatment strategies, respectively. We simulated the model to determine the minimum number of infections as a function of δR and α in each strategy. Simulations in Figure 6(a) and 6(b) show contour plots for the ratio Fop/Foc with two different ranges of α. Simulation results for this ratio indicate that as the transmissibility of the resistant strain increases above a certain threshold, the ratio Fop/Foc decreases below 1, implying that the optimal time-dependent treatment profile outperforms the optimal constant strategy in reducing the final size. However, the corresponding reduction in the final size depends significantly on the rate of resistance emergence. We also observe that, as δR increases, the change in the ratio Fop/Foc is less pronounced for variation of α in the range 10−6 − 10−3 (Figure 6(b)) compared to the range 10−3 − 10−1 (Figure 6(a)).


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

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

Contour plots for the ratio Fop/Foc for α in the range (a) 10−3 − 10−1 and (b) 10−6 − 10−3. Contour plots for the ratio Kop/Koc for α in the range (c) 10−3 − 10−1 and (d) 10−6 − 10−3. Other parameter values are given in Table 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Contour plots for the ratio Fop/Foc for α in the range (a) 10−3 − 10−1 and (b) 10−6 − 10−3. Contour plots for the ratio Kop/Koc for α in the range (c) 10−3 − 10−1 and (d) 10−6 − 10−3. Other parameter values are given in Table 1.
Mentions: To compare the outcomes of optimal scenarios in the two treatment profiles simulated in Figure 5, we defined Fop and Foc to be the final sizes of the epidemic in the time-dependent and constant treatment strategies, respectively. We simulated the model to determine the minimum number of infections as a function of δR and α in each strategy. Simulations in Figure 6(a) and 6(b) show contour plots for the ratio Fop/Foc with two different ranges of α. Simulation results for this ratio indicate that as the transmissibility of the resistant strain increases above a certain threshold, the ratio Fop/Foc decreases below 1, implying that the optimal time-dependent treatment profile outperforms the optimal constant strategy in reducing the final size. However, the corresponding reduction in the final size depends significantly on the rate of resistance emergence. We also observe that, as δR increases, the change in the ratio Fop/Foc is less pronounced for variation of α in the range 10−6 − 10−3 (Figure 6(b)) compared to the range 10−3 − 10−1 (Figure 6(a)).

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