How could preventive therapy affect the prevalence of drug resistance? Causes and consequences

Various forms of preventive and prophylactic antimicrobial therapies have been proposed to combat HIV (e.g. pre-exposure prophylaxis), tuberculosis (e.g. isoniazid preventive therapy) and malaria (e.g. intermittent preventive treatment). However, the potential population-level effects of preventative therapy (PT) on the prevalence of drug resistance are not well understood. PT can directly affect the rate at which resistance is acquired among those receiving PT. It can also indirectly affect resistance by altering the rate at which resistance is acquired through treatment for active disease and by modifying the level of competition between transmission of drug-resistant and drug-sensitive pathogens. We propose a general mathematical model to explore the ways in which PT can affect the long-term prevalence of drug resistance. Depending on the relative contributions of these three mechanisms, we find that increasing the level of coverage of PT may result in increases, decreases or non-monotonic changes in the overall prevalence of drug resistance. These results demonstrate the complexity of the relationship between PT and drug resistance in the population. Care should be taken when predicting population-level changes in drug resistance from small pilot studies of PT or estimates based solely on its direct effects.


A Equations
The states and parameters used here are the same as those described in Table 1 in the main text.
S P T = f S − wS P T − β P T S (I S + I P T S + T S )S P T − β R (I R + I P T R + T R )S P T − µS P Ṫ L S = β S (I S + I P T S + T S )(S + xL R + xR) − xβ R (I R + I P T R + T R )L S − (k S + µ + f l )L S + wL P T Ṡ L R = β R (I R + I P T R + T R )(S + xL S + xR) − xβ S (I S + I P T S + T S )L R − (k R + µ + f l )L R + wL P T Ṙ L P T S = β P T S (I S + I P T S + T S )(S P T + xL P T R + xR P T ) − xβ R (I R + I P T

B Calculating DR Effective Reproductive Number
This section refers to states and parameters described in Table 1 in the main text. The effective reproductive number is the number of secondary infectious cases produced by a single infectious individual over the course of their infectious period. We derived the effective reproductive number of the DR strain R RE at equilibrium from first principles using the following equation: We walk through each of the individual components of this equation below. β R is the transmission parameter for the DR strain, as described in the main text. D, the average duration of infectiousness with the DR strain, is the sum of two terms: 1) the average length of stay in the untreated infectious compartment and 2) the average length of stay in the treated infectious compartment given that the individual initiates treatment prior to death. This expression is given below: P 0 , the probability of progressing from latent to active disease for individuals not on preventive therapy at the time of infection, is the sum of the probability of progressing before leaving L R , the probability of starting preventive therapy and then progressing before leaving L P T R , the probability of starting preventive therapy and then stopping preventive therapy and then progressing before leaving L R , and so on: This expression for P 0 captures all of the possible paths from the latent state to the infectious state and hence captures the total probability of progression from latency to active DR disease. If we let z = wf l /(D 0 D P T ) then the expression for P 0 simplifies to We can similarly derive the expression for P P T , the probability of progressing from latent to active disease for individuals on preventive therapy at the time of infection, which simplifies to Finally, θ 0 R is the fraction of individuals who are susceptible to infection with the DR strain and not currently on PT: θ 0 R = S + xR + xL S and θ P T R is the fraction of individuals on PT who are susceptible to infection with the DR strain: Individuals already infected with the DR strain are not included here, even though they may be reinfected with the DR strain, because they do not change states upon reinfection.

C DR Effective Reproductive Number Components
Changing the coverage of preventive therapy changes the DR effective reproductive number in two ways: by affecting the proportion of people infected with the DR strain who progress to active DR disease, and by affecting the proportion of the population that is susceptible to the DR strain.
Here we show how each of these components are affected by changing PT coverage, using notation defined earlier in the appendix and in Table 1 in the main text.
The proportion of people infected with the DR strain who progress to active DR infection depends on the DS infection rate, which itself depends on the proportion of the population receiving preventive therapy. To produce a population average, we used the formula The results are shown in Supplemental Fig 1. The proportion of DR infected persons who progress to active infection with the DR strain increases with increasing PT coverage.  PT start rate (f) DR susceptibility metric