Limits...
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.

Show MeSH

Related in: MedlinePlus

Delay in start of treatment in the time-dependent profile as a function of δR and α to minimize the epidemic final size is shown for (a) K = 8%; (b) K = 12%; and (c) K = 16%. Optimal level in the constant treatment profile as a function of δR and α to minimize the epidemic final size is shown for (d) K = 8%; (e) K = 12%; and (f) K = 16%. Other parameter values are given in Table 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3753656&req=5

Figure 5: Delay in start of treatment in the time-dependent profile as a function of δR and α to minimize the epidemic final size is shown for (a) K = 8%; (b) K = 12%; and (c) K = 16%. Optimal level in the constant treatment profile as a function of δR and α to minimize the epidemic final size is shown for (d) K = 8%; (e) K = 12%; and (f) K = 16%. Other parameter values are given in Table 1.

Mentions: The effect of relative transmissibility of the resistant strain (δR) on the optimal treatment level has been investigated in previous work [12–14,23,26,28,31]. However, as shown in our simulations, the rate of resistance emergence (α) also plays a critical role in identifying the optimal treatment profile for a limited drug stockpile. To illustrate the combination effect of α and δR, we simulated the model to determine the optimal treatment rate (i.e. time dependent with a switch) for different sizes of drug stockpile (Figure 5(a)–(c)). These simulations indicate that when δR is relatively low (i.e. remains below 0.6 in these scenarios), the optimal control suggests that the minimum final size corresponds to the start of treatment at the onset of epidemic without any delay. However, as δR increases above a certain threshold, then the resistant strain gains a competitive advantage, and the size of stockpile becomes important in determining the delay in start of treatment. For some values of δR (0.6 < δR < 0.8 in these scenarios), as the size of drug stockpile increases, a longer delay is required to minimize the total number of infections (Figure 5(b)–(c)). This delay is shorter for higher values of α. For relatively high values of δR (δR > 0.8 in these scenarios), the rate of resistance emergence (α) has very little impact in determining the optimal timing for switch (regions to the right side of δR = 0.8 in Figure 5(a)–(c)).


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

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

Delay in start of treatment in the time-dependent profile as a function of δR and α to minimize the epidemic final size is shown for (a) K = 8%; (b) K = 12%; and (c) K = 16%. Optimal level in the constant treatment profile as a function of δR and α to minimize the epidemic final size is shown for (d) K = 8%; (e) K = 12%; and (f) K = 16%. 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 5: Delay in start of treatment in the time-dependent profile as a function of δR and α to minimize the epidemic final size is shown for (a) K = 8%; (b) K = 12%; and (c) K = 16%. Optimal level in the constant treatment profile as a function of δR and α to minimize the epidemic final size is shown for (d) K = 8%; (e) K = 12%; and (f) K = 16%. Other parameter values are given in Table 1.
Mentions: The effect of relative transmissibility of the resistant strain (δR) on the optimal treatment level has been investigated in previous work [12–14,23,26,28,31]. However, as shown in our simulations, the rate of resistance emergence (α) also plays a critical role in identifying the optimal treatment profile for a limited drug stockpile. To illustrate the combination effect of α and δR, we simulated the model to determine the optimal treatment rate (i.e. time dependent with a switch) for different sizes of drug stockpile (Figure 5(a)–(c)). These simulations indicate that when δR is relatively low (i.e. remains below 0.6 in these scenarios), the optimal control suggests that the minimum final size corresponds to the start of treatment at the onset of epidemic without any delay. However, as δR increases above a certain threshold, then the resistant strain gains a competitive advantage, and the size of stockpile becomes important in determining the delay in start of treatment. For some values of δR (0.6 < δR < 0.8 in these scenarios), as the size of drug stockpile increases, a longer delay is required to minimize the total number of infections (Figure 5(b)–(c)). This delay is shorter for higher values of α. For relatively high values of δR (δR > 0.8 in these scenarios), the rate of resistance emergence (α) has very little impact in determining the optimal timing for switch (regions to the right side of δR = 0.8 in Figure 5(a)–(c)).

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