INTRODUCTION

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Recurrent herpes labialis (RHL), caused by herpes simplex virus type 1 (HSV-1) affects 15 to 40% of adults in countries around the world (23). Primary oral-facial infection with HSV-1 usually occurs in childhood and may either be asymptomatic or result in oral lesions. Following primary infection, the virus establishes latent infection in the sensory ganglia of the trigeminal nerve. Subsequently, latent HSV-1 may reactivate and spread back to the periphery to initiate a recurrent episode of disease (cold sore). In immunocompetent individuals, HSV-1 replication is self-limited and the cold sore disappears within about 10 days or less (50).

The nucleoside analogues acyclovir (ACV) and penciclovir (PCV) and their respective oral prodrugs, valaciclovir and famciclovir, are used to treat infections caused by HSV-1 or HSV-2 (generally associated with genital herpes). There are two approaches to the therapy of RHL: episodic treatment of a single symptomatic outbreak, which reduces the duration of symptoms and viral shedding (2, 50, 52, 53), and long-term suppressive therapy, which reduces the frequency of recurrences (44, 51). Although neither ACV nor PCV is approved for long-term suppression of RHL, topical PCV has been approved in the United States for treatment of RHL, and in other countries topical ACV and topical PCV are available. The same agents are also effective for the treatment of genital herpes, (35, 42, 45, 58). For both genital and labial herpes, treatment fails to eradicate latent virus and episodes continue to recur periodically after treatment is discontinued (50).

Resistance to ACV is readily selected in vitro and usually results from mutation in the thymidine kinase gene, leading to an absence or reduced expression of thymidine kinase and failure to activate ACV (28). Less commonly, resistance is attributable to a mutation in the viral DNA polymerase (17). ACV-resistant HSV is usually cross-resistant to PCV (11). Based on surveys among immunocompetent individuals, generally with genital herpes, ACV-resistant HSV is rare, appearing in about 0.3% of patients as measured by a plaque reduction assay (PRA) (15; R. Sarisky, K. Esser, R. Saltzman, L. Locke, R. Boon, T. Bacon, and J. Leary, Abstr. 38th Intersci. Conf. Antimicrob. Agents Chemother., abstr. H-10, p. 317, 1998). Because of the self-limiting nature of HSV reactivations in these patients, resistance has minor clinical consequences and resistant virus may occur only transiently (22). In severely immunocompromised people, however, resistance is more common. HSV can cause severe disease in these individuals, and resistance can have more serious clinical consequences (41).

This paper describes the results of mathematical modeling designed to assess the effects of antiviral treatment of RHL on the transmission dynamics of drug-sensitive and drug-resistant HSV-1 infections. Related models have been used recently to assess the impact of antiviral drug use on transmission of and resistance in genital herpes (7) and influenza (56). The models are used to answer two specific questions.

First, to what degree does antiviral treatment reduce the transmission of drug-sensitive HSV-1? This question is addressed, using a basic model, by considering three different scenarios of antiviral use. As a baseline, we consider a hypothetical case in which no antivirals were used to treat HSV-1. This baseline is then compared to the effects of current usage, as measured by recent antiviral prescription data from the United States. We then consider the effects of a large increase in antiviral usage, with specific reference to a substantial increase in topical PCV usage for the treatment of RHL, such as would be anticipated if this treatment were available over the counter (OTC).

Second, to what degree does antiviral treatment promote the development and spread of drug resistance in the community of hosts infected with HSV-1? To address the additional complexities of transmission of resistance, we use an expanded model, which adds several features to those of the basic model, most importantly, age structure, the existence of an immunocompromised class, and the possibility that treatment of an RHL episode can result in acquired resistance in a treated host.

(This work was presented in part at the 39th Interscience Conference on Antimicrobial Agents and Chemotherapy, San Francisco, Calif., 26 to 29 September 1999.)

	MATERIALS AND METHODS

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Basic model. The structure of the basic mathematical model is shown in Fig. 1, and the equations are given below. This compartmental model considers individuals in one of three states: susceptible (never infected with HSV-1), infected with sensitive virus, and infected with resistant virus. The number of individuals in each category is denoted by S, I_S, and I_R, respectively. Individuals are born into the susceptible class at rate b per day and live for an average of 1/u days. The overall framework is reflected in the following equations: dS/dt = b  (u + _Sw_SI_S + _Rw_RI_R)S; dI_S/dt = _Sw_SI_SS  uI_S; and dI_R/dt = _Rw_RI_RS  uI_R.

View larger version (11K): [in this window] [in a new window]   FIG. 1.   Structure of a basic, compartmental model of HSV-1 transmission. (a) Overall framework, in which individuals are either susceptible (S), infected with sensitive virus (IS), or infected with resistant virus (IR). (b) Proportions of individuals infected with sensitive virus who are asymptomatic (SA), symptomatic and untreated (SU), or symptomatic and treated (ST). Infectiousness may differ among individuals in these three states. Untreated individuals remain infectious for longer than untreated individuals. (c) Once infected with resistant virus, individuals may be asymptomatic (a proportion, RA), or symptomatic (a proportion, RS); treatment of these persons has no effect.

Expanded model. The expanded model is a generalization of the basic model but incorporates four major changes.

(i) Addition of an immunocompromised class. In effect, the basic model of Fig. 1 has been duplicated to include variables for a class of immunocompromised individuals that correspond to variables for each class of immunocompetent individuals. Individuals enter an immunocompromised class from the corresponding immunocompetent class at a per capita rate of h per day. Immunocompromised individuals differ from immunocompetent individuals in three ways. First, they are assumed to be more susceptible to new infections by a factor, . Second, they may contribute more or less to transmission to other individuals by a factor, , than an equivalent immunocompetent person (they may be more infectious because of greater viral shedding; on the other hand, their condition may make them more isolated and therefore less likely to transmit their infection). Finally, their life spans are assumed to be shorter than those of immunocompetent people.

(ii) Dual infection is possible. In this expanded model, it is assumed that an individual already infected with sensitive HSV-1 can be newly infected with resistant HSV-1 and vice versa. The number of individuals dually infected (with both kinds of virus) is indicated by the variable I_D. Dual infection is known to be rare but possible in HSV-2 (12, 46); data for HSV-1 are not available, and we consider both zero and low rates in the model. Dual infection, like primary infection, occurs at a rate proportional to the rates of transmission (or force of infection) of sensitive and resistant viruses, but the model makes the assumption that individuals in the immunocompetent class acquire second infections at a rate  times the rate at which they would acquire the infection if they were not already infected with the other strain. Because it is thought that infection (seropositivity) with an HSV-1 strain offers considerable protection against infection with another HSV-1 strain,  is much smaller than 1. The corresponding parameter for the immunocompromised class, ', is assumed to be greater than  but still smaller than 1.

(iii) Age structure. HSV-1 may be acquired relatively early in life, and infected individuals may continue to be infectious throughout their life spans. Because the duration of infectiousness and the duration of life are comparable for this infection, we felt it was necessary to model host demography with type 2 survivorship, which is more realistic than the exponential (type 1) survivorship used for mathematical convenience in the basic model (3). The expanded model assumes that all immunocompetent individuals live for 70 years and then die. For immunocompromised individuals, type 1 survivorship is maintained. Here, an average life span of 10 years in the immunocompromised state is assumed. This assumption is made to be conservative, as longer life spans for immunocompromised persons increase their ability to spread resistant virus.

(iv) Acquired resistance. Drug-sensitive infections in patients treating a recurrence with topical PCV may convert to drug-resistant infections. We assume that this occurs with probability m in each treated episode. Acquired resistance is thought to occur at an elevated rate in immunocompromised individuals (15, 24, 25), and this assumption is also reflected in the model.

View larger version (17K): [in this window] [in a new window]   FIG. 2.   Structure of an expanded model with consideration of age structure, immunocompromised class, and dual infection. As with the basic model, S denotes the number of individuals susceptible to HSV-1, IS denotes the number infected with sensitive virus only, IR denotes the number infected with resistant virus only, and ID denotes the number dually infected with both resistant and sensitive viruses. Within each infected compartment, transitions among asymptomatic, symptomatic treated, and symptomatic untreated are as described for the basic model (Fig. 1b to c). All quantities referring to immunocompromised persons are marked with a prime. *, type 2 survivorship; all deaths are at age 70.

Parameter estimates. The parameters of the basic model (Table 1) were estimated from published data. The precision of these estimates varies, depending on the quantity and reliability of data available. For each parameter, we have made a best estimate based on a consensus of the data, as well as a range of plausible values where appropriate. Where uncertainty exists, the range has been chosen to encompass values that are reasonable in light of available evidence.

Acquired resistance. A key parameter of the expanded model is m, the probability that treatment of one RHL episode in an immunocompetent individual results in permanent acquired resistance in that individual. Because of the importance of this parameter, we describe the estimation of its possible values in detail. At present, it is unclear whether resistance can be acquired when a symptomatic episode of sensitive HSV-1 in an immunocompetent person is treated with a nucleoside analogue. There are four reports in which treatment of an immunocompetent host may have resulted in the acquisition of resistance in HSV-1 or HSV-2 (22, 33, 38, 58, 59). In none of these is it certain whether treatment itself was responsible for the appearance of resistant virus. More than 1,900 immunocompetent patients have been monitored in clinical trials of various nucleoside analogues for symptomatic treatment or suppressive therapy of HSV-1 and HSV-2, and there has not been a significant increase in antiviral resistance in treated patients compared to that in untreated patients (or compared to that in matched pretreatment isolates) (1, 15, 18-20, 24, 29, 34, 35, 38; R. Sarisky et al., 38th ICAAC). If one assumes that acquired resistance occurred in 0 of 1,900 episodes (a conservative estimate of the total number, taking into account the fact that some clinical trial data seem to be described in more than one published paper and ignoring the possibility that more than one episode may have occurred in some patients) treated with nucleoside analogues, then the 95% confidence interval (CI) for m, the probability of acquired resistance per treated episode, using the binomial assumption is 0 to 0.0016. We use this interval as the possible interval for m in our model, with the following two caveats.

Evaluation of the model. The basic model was evaluated analytically for particular parameter values to determine the effect of treatment on the prevalence of HSV-1 infection. Uncertainty about key parameters was quantified by using the range of parameter values described below. The expanded model was evaluated numerically using a FORTRAN program, which treated the partial differential equations as a set of coupled ordinary differential equations in which each 1-year age class was a separate compartment and integrated the differential equations by the Euler method. Again, different parameter values were used to quantify the impact of different assumptions about acquired resistance and transmission of resistance.

	RESULTS

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Effect of antiviral treatment on transmission and prevalence of drug-sensitive HSV-1. The basic model was used to estimate the effect of treatment on the transmission and prevalence of drug-sensitive HSV-1. The transmissibility of HSV-1 can be measured by the basic reproductive number, R₀. The basic reproductive number of an infection is defined as the average number of secondary cases that would be generated by a single infected individual placed into a completely uninfected population at equilibrium and is given for this model (for sensitive virus) by the following equation:

(1)

For an infection like HSV-1, the basic reproductive number can be estimated (3) from the equation

(2)

or from the equation

(3)

Based on available age-seroprevalence data (48, 63), these equations yield an approximate value for R₀ in the range of 2 to 4.5.

Scenario 1: antiviral usage at current levels. The model predicts that current levels of antiviral usage have a small impact on the transmission and prevalence of sensitive HSV-1. For any given reduction in the basic reproductive number R₀, there is a corresponding reduction in the equilibrium seroprevalence of HSV-1, given by equation 2 above. In all cases, the reduction in seroprevalence is smaller than the reduction in R₀. Figure 3a shows the estimated reductions in R₀ (left-hand scale) and equilibrium seroprevalence (right-hand scale; dashed lines) that result from current antiviral usage. Depending on the assumptions, current antiviral use reduces transmission by between 0 and 2.5%, which translates into a reduction in prevalence of less than 1%.

View larger version (23K): [in this window] [in a new window]   FIG. 3.   Predicted effect of antiviral treatment on transmission of drug-sensitive HSV-1. In both panels a and b, reduced transmission is shown as the percentages of reduction in the basic reproductive number, R0 (left-hand scale), and in equilibrium seroprevalence (right-hand scale; dashed lines). (a) Current use. On the x axis are the percentages of current use that are directed against RHL episodes, rather than other conditions. The three lines reflect different assumptions about the values of parameters of the model. In the upper line (greatest reduction in transmission), ST = 0.1, SA = 0, and dST = 0.85; in the middle line, ST = 0.5, SA = 0.02, and dST = 0.4; and in the lower line (smallest reduction in transmission), ST = 1, SA = 0.05, and dST = 0.26). Other parameters are as shown in Table 1, scenario 1. (b) Increased use. Reductions are shown for the use of topical PCV to treat up to 30% of all RHL episodes (x axis), with different assumptions being made about the transmissibility of HSV-1 from treated symptomatic and asymptomatic hosts relative to that from untreated symptomatic hosts. In the upper line (greatest reduction in transmission), ST = 0.1 and SA = 0; in the middle line, ST = 0.5 and SA = 0.02; and in the lower line (smallest reduction in transmission), ST = 1 and SA = 0.05). Other parameters are as in Table 1, scenario 2.

Scenario 2: increased antiviral usage. If antiviral use for RHL were increased substantially by introduction of topical PCV OTC, the model predicts that the effect on transmission and prevalence would be larger than the effect of current treatment but that it would remain modest in absolute terms. Figure 3b shows the effects on transmission of HSV-1, assuming that topical PCV is used to treat up to 30% of RHL episodes. As before, the left-hand scale shows the percentage reduction in R₀ while the right-hand scale shows the corresponding reduction in equilibrium seroprevalence. Taking the intermediate set of parameters, the reduction in seroprevalence of HSV-1 is expected to be less than 5%, even if 30% of RHL episodes are treated.

Effects of antiviral use on the spread of resistant infections. The expanded model was used to analyze the effect of antiviral use on the spread of resistance.

Effects of current antiviral use. This model predicts that at current levels of antiviral use, the prevalence of resistance will remain low. In the absence of antiviral use, the basic reproductive number of sensitive infections is expected to be greater than that of resistant infections, as long as resistant infections have even a small (1 to 2%) disadvantage in their rate of transmission. As mentioned in Materials and Methods (see also Tables 1 and 4), the magnitude of this cost of resistance is unknown but appears to be considerable for many resistant isolates. As the amount of antiviral usage increases, the basic reproductive number of sensitive infections (R_0S) declines while the corresponding number for resistant infections (R_0R) stays constant. The reduction in R_0S as a result of treatment can be seen as a burden imposed by treatment on the fitness of the sensitive virus. This burden can be directly compared to the cost (c), the proportional reduction in transmission from hosts infected with resistant virus compared to that from hosts infected with sensitive, untreated virus. To a good approximation, if the burden of treatment on the fitness of sensitive infections is greater than the cost of resistance, then resistant infections will be able to spread in the population. If the cost of resistance is greater, then resistant infections will remain at low levels or decline.

Effects of increased antiviral use. We first performed exploratory simulations using the parameter ranges described in Table 3. From these simulations, it was clear that the probability of acquired resistance per treated RHL episode, m, is the single most important factor determining whether and how fast resistance increases in the population following an increase in the rate of topical PCV use. As described in Materials and Methods, the 95% CI for m estimated from a combination of studies is (0, 0.0016). Therefore, we present the simulation results separately for four different values of this key parameter: 0, 0.0016 (1 in 6,250 treated episodes or 1/10 of the maximum of the 95% CI), 0.0004 (1 in 2,500 treated episodes or 1/4 of the maximum of the 95% CI), and 0.0016 (1 in 625 treated episodes or the maximum of the 95% CI). These results are shown in Fig. 4.

View larger version (41K): [in this window] [in a new window]   FIG. 4.   Changes in the prevalence of infection with resistant HSV-1 following an increase in topical PCV usage. (a to d) Increasing probabilities of acquired resistance per treated episode in an immunocompetent host (m), within the rough 95% CI estimated in the text, with m = 0, (a), m = 1/6,250, (b), m = 1/2,500, (c), and m = 1/625 (d). Curves (from top to bottom within each panel) represent pessimistic, moderate, and optimistic assumptions concerning the selective pressure (antiviral use, effect of use in reducing transmissibility, etc.). In each scenario, it is assumed that 0.3% of HSV-1-infected persons are infected with resistant virus at time zero but that the starting levels of prevalence of resistant infection are different under different scenarios (and less than 0.3%) because the figure shows the prevalence of resistant infection (prevalence of HSV-1 infection times the proportion of individuals who are resistant) in the whole population, and the levels of prevalence of HSV-1 infection are different in different scenarios.

	DISCUSSION

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We have used a mathematical model to analyze the effect of antiviral treatment of RHL on the transmission dynamics of HSV-1. Two basic questions were addressed: (i) to what degree does antiviral treatment reduce the transmission of the virus, thereby providing a public health benefit in the form of reduced prevalence of HSV-1 infection, and (ii) does the selective pressure imposed by antiviral treatment cause the spread of antiviral-resistant HSV-1 infections, and if so, how fast will these infections spread? We first modeled the effects of current antiviral use and then used the model to predict the effects on transmission and resistance in HSV-1 if there were a substantial increase in the use of topical PCV to treat recurrent herpes labialis, such as might be expected if PCV was approved for OTC sales.

Our principal findings were as follows. First, current antiviral use has at most a small effect on the transmission and prevalence of HSV-1. Consequently, it also exerts a small selective effect in favor of antiviral resistance, so the model predicts that current antiviral use is unlikely to increase the prevalence of antiviral resistance. This prediction is consistent with recent surveillance data largely from patients with genital herpes (15, 43).

Second, a substantial increase in antiviral treatment of RHL would produce only a modest reduction in the transmission and prevalence of HSV-1. Estimating this effect precisely is difficult, primarily because adequate data on the relationship between symptomatic and asymptomatic viral shedding and also on transmission of HSV-1 infection are not available (9, 65). Nonetheless, using the best available estimates (the middle line of Fig. 3b), the model predicts that the prevalence of HSV-1 infection would decline by less than 5%, even if 30% of all recurrences were treated with topical PCV.

Third were the effects of increased antiviral use on resistance. The most important parameter determining the rate at which the prevalence of resistant HSV-1 rises following an increase in antiviral usage is m, the probability that a treated RHL episode will result in acquired resistance. Unfortunately, this parameter is also the most uncertain; with approximately 1,900 patients studied for emergence of resistance during nucleoside analogue treatment of HSV infection, the 95% CI for m is (0, 0.0016), corresponding to the emergence of acquired resistance in between 0 and 1 in 625 treated episodes. If the true probability of acquired resistance is less than or equal to about 1 in 6,250 treated episodes (10% of the maximum value), then the increase in resistant infections will be very slow, remaining below 1% prevalence after 50 years even if the selective pressure in favor of resistance is very strong. If the true probability of acquired resistance takes a value intermediate between these figures, approximately 1 in 2,500 patients, then rapid increases in the prevalence of resistant infection will occur only if the selective pressure for resistance is very high. If the true probability of acquired resistance were indeed 1 in 625 treated episodes, then the spread of resistance could be faster; in the extreme, the prevalence of resistant HSV-1 could exceed 1% within less than 20 years. However, we note that even under these assumptions, which are pessimistic with respect to both acquired resistance and selective pressure, the predicted rate of increase is still considerably slower than that observed (4, 5, 8) or predicted (10, 56) for many other viral and bacterial pathogens.

In determining the optimistic and pessimistic values for the parameters that underlie the selective pressure, we used values consistent with available data that would produce the slowest and fastest increases in the prevalence of resistant infection, respectively; the moderate values were intermediates between these extremes. In some cases, the choice of optimistic and pessimistic values was counterintuitive. For example, in the case of _SA, the relative contribution of asymptomatic individuals to transmission, one might expect that high values would result in a faster rise in resistance. In fact, the fastest rise in resistance occurs when asymptomatic individuals contribute least to transmission. Topical PCV is applied only to symptomatic recurrences of RHL, so when symptomatic persons are the main sources of transmission, treatment exerts the maximum selective pressure against sensitive virus. Similarly, the greatest selective pressure (and therefore the fastest rise in resistance) occurs when treatment is highly effective in reducing transmission of sensitive virus.

The predictions of the model are consistent with the observation that the prevalence of resistance in HSV-1 has remained relatively flat, despite almost 20 years of nucleoside analogue use. The modeling framework used here demonstrates, perhaps counter to intuition, that although current usage of nucleoside analogues looks large in absolute terms (see "Parameter estimates" above), the selection exerted by present usage in favor of resistance (in immunocompetent hosts) is rather small. Another prediction of the model that was surprising, at least to its authors, is the sensitive dependence of its predictions on the probability of emergence of resistance within treated, immunocompetent hosts. The continued validity of the model's predictions will be tested over time as levels of nucleoside analogue use for and resistance in HSV-1 are monitored.

Our predictions may be compared to the predictions of other, recently published models of virus transmission and antiviral treatment. Blower et al. (7) study oral ACV treatment of genital herpes caused by HSV-2. In contrast to our predictions for labial herpes, they find that widespread use of ACV for treatment of genital herpes might substantially reduce the prevalence and incidence of the infection. Several biological differences between HSV-1 and HSV-2 account for this divergent prediction, including route of transmission, seroprevalence, and frequency of recurrences. In addition, Blower et al. consider higher levels of antiviral treatment (up to 50%) than those considered here; another model of ACV treatment of HSV-2 found that treatment would have to be widespread and continued for a long period in order to reduce HSV-2 transmission substantially (62). On the question of drug resistance, our conclusions are in general accord with those of Blower et al. in predicting that drug resistance will remain rare (less than 5% of infections over 50 years), even under pessimistic assumptions.

In contrast to these models of HSV infection, models of amantadine or rimantadine treatment in an influenza epidemic predict extremely rapid increases in resistance, reaching 10% within weeks of the onset of treatment (56).

There are at least four key reasons why the emergence of resistance is expected to be slower for HSV-1 or HSV-2 than for influenza virus. (i) Acquired resistance is less common. Despite the uncertainty about just how rare acquired resistance is, it is clear that it is less common in treated HSV-1 patients than the 20% assumed for amantadine and rimantadine treatment of influenza (56). As we have seen, the probability of acquired resistance is crucial to the rate of ascent of resistance in the population. (ii) HSV infection, and presumably infectiousness, is life-long (64). The time scale on which resistance increases in a population is proportional to the duration of the infectiousness (10), so long-lived infections like HSV-1 have much slower dynamics than acute infections. (iii) Many resistant HSV-1 mutants may be less transmissible (less infectious and/or less likely to reactivate from latency) than sensitive wild-type virus, as shown by reduced virulence in animal models (16, 27). (iv) Treatment of sensitive infections causes a relatively modest reduction in shedding and (presumably) transmission. Topical PCV reduces the duration of shedding by 25% in patients with RHL (52), which means that the selective pressure in favor of resistance is relatively weak. This finding is compounded by the fact that treatment does not preclude future episodes of shedding, so that the impact of a single treatment episode on the total transmission from an infected individual is very small.

To address the uncertainty surrounding the predictions of the rate of the ascent of resistance in the population, it is crucial that ongoing surveillance for resistance be targeted to long-term monitoring of virus isolates from individuals who repeatedly treat recurrences with antiviral drugs. Such studies would be most likely to yield maximal information about acquired resistance per unit effort. Furthermore, methodologies should be developed and standardized to measure subpopulations of resistant viruses within a heterogeneous virus sample; such methods would be valuable for testing whether there are gradual increases in the proportion of resistant viruses during successive rounds of treatment. One such method, the plating efficiency assay (39), is currently being evaluated alongside the PRA (J. Leary and R. Sarisky, unpublished data).