Population-level mathematical modeling of antimicrobial resistance: a systematic review

We undertook a systematic search and review of publications relevant to the transmission modeling of AMR. Searches were carried out in PubMed-MEDLINE, Scopus, Web of Science, and Embase. Publications were limited by date (January 1, 2006–December 31, 2016) and journal type (original research and review articles only). Data extraction was initially carried out on November 15, 2016 and updated in January 2018. The search query included terms specific to transmission models, resistance issues, and individual pathogens known to acquire resistance (see Additional file 1 for details of the query). We removed duplicate publications and continued with the selection of relevant publications according to the inclusion/exclusion criteria listed below. A summary of the process is outlined in the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-analyses) diagram in Fig. 2 and in Additional file 2.

We included any mathematical or computational models describing AMR in an infectious disease pathogen and considering transmission at the population level (i.e., publications on between-host transmission dynamics). We excluded within pathogen/host models of resistance (e.g., exclusively within-host models based on in vitro data), pharmacokinetic-pharmacodynamic models (i.e., pharmacological models focused on optimizing drug dosage that did not include a transmission component), molecular modeling studies (studies focused on molecular structure of chemical compounds), reviews that did not present original work, non-journal articles or reviews (poster or conference abstracts), and descriptive statistical models not incorporating mechanistic principles (such as models based on probability distributions, e.g., regression, clustering analysis).

An initial round of title and abstract screening was performed by AMN. Articles identified as potentially relevant were then reviewed by both AMN and CV, and the publication list for full-text analysis was agreed upon by consensus. Full texts for 313 articles were then retrieved, evaluated by AMN, and relevant data was extracted for further analysis (see below). For details on the number of articles excluded at each step, see Fig. 2.

The following data were retrieved from articles: disease system (type: viral (V), bacterial (B), parasitic (P), fungal (F) or non-specific (NS)); drug type; control measures (pharmaceutical and non-pharmaceutical interventions, vaccines, behavioral); location (year, country, WHO region); host population: type (human, animal, plant) and setting (school/family, hospital, community, farm, etc.); data: data used for parameterization (epidemiological, clinical, behavioral, demographic, geospatial), data availability (public, on request, private); methodology: model class (compartmental or individual-based), inference method, and study type (explicative, predictive, interventions vs. forecasting); and metadata (authors, institutions, funding). Pathogen types were also later compared with the published WHO and center for disease control (CDC) lists of most urgent threats in AMR [1, 15].

A goal of our systematic review was to explore trends in the publication output for AMR modeling studies and their impact in the field, as AMR is emerging as a global health threat. Our review focused on the period 2006–2016; to explore publication trends in earlier years, we used a prior review by Temime et al. [11] which covered the period 1993–2006. Further, for comparison with a related area of infectious disease modeling, we compiled trends in publication of individual-based transmission models (defined as a model tracking the characteristics of an individual, including infection and transmission, over time), based on a recent systematic review [16]. In addition to the volume of AMR modeling publications, we assessed the impact of these publications in the field using the metric field-weighted citation impact (FWCI) [17]. The FWCI is the ratio between the number citations for a specific article and the average number of citations received by similar articles in the same field, type, and year of publication, thus making values comparable across these three variables. A FWCI greater than 1.0 indicates that publications have been cited more than would be expected; for example, a score of 1.2 means that an article has been cited 20% more than average. It should be noted that a FWCI score can vary over time and that data in our manuscript is based on a snapshot of the Scopus database taken on November 21, 2018.

We used a seminal 2016 Review on Antimicrobial Resistance as a framework to classify interventions [18]. The report identified 10 intervention categories, of which only the first six were relevant to our study: (1) education or awareness campaigns, (2) improved hygiene and infection control, (3) reduction in use of antimicrobials, (4) improved surveillance of resistance, (5) improvement and development of rapid diagnostics, and (6) use of antimicrobial alternatives such as vaccines and alternatives. We also added a seventh category to consider antimicrobial regimen changes, as this is an area of high interest for public health (e.g., antimicrobial switching, cycling, introduction of new drug class).

Further, we identified whether interventions were modeled on a “micro” (institution level) or “macro” level (structural or policy interventions that might affect large populations, communities, countries, or regions). We also assessed whether the aim of the study was to prevent the development/acquisition of AMR (de novo resistance) or direct transmission of a resistant pathogen.

We found an increasing trend (Fig. 3) in the annual number of AMR modeling studies between 2006 and 2016 (linear trend, slope = 1.5, R² = 0.43), building off the steady increase shown by Temime et al. [11]. Since 2013, the pace of AMR modeling publications has leveled off at around 25 articles/year. In contrast, as described by Willem et al. [16], publications on individual-based models of infectious diseases have experienced a faster increase over the same time period (linear trend, slope = 7, R² = 0.66), with on average three to four times more articles published on infectious disease related individual-based models than on AMR (Fig. 3). A histogram showing the number of AMR modeling articles published per year since 1990 can be found in Additional file 1: Fig. S1.

In addition to overall publication output, we assessed the influence of AMR modeling publications in the field using the FWCI score. The three publications with the highest FWCI during this period had a FWCI greater than 10 (two articles on TB [19, 20] and one on pandemic flu [21]). Excluding these three highly cited outliers, we found that the median FWCI for publications ranged between 0.47 and 2.65, with an overall median of 0.96, indicating that AMR modeling publications are being cited at a rate on par with other studies in their field (Additional file 1: Figure S2).

Approximately 65% of the AMR studies focused on bacterial diseases, 25% on viral diseases, 13% on parasitic diseases, and 2% on plant fungal pathogens. The top five pathogens most prominently studied were MRSA (25%), TB (16%), Plasmodium falciparum (8%), HIV (13%), and influenza (11%). For a detailed list of pathogens studied in each publication, see Additional file 1: Table S1. There was no significant time trend in the modeling of specific pathogens (Additional file 1: Figure S3).

Of the 273 publications considered in our review, 89% (n = 234) concerned human hosts, 7% (n = 18) focused on animal diseases, and 2% (n = 5) considered plant hosts. Only 2% (n = 6) addressed transmission between humans and animals in the same model. Animal transmission studies were mainly on animals of agricultural importance, although one explored transmission between humans and companion animals [22]. Only one study modeled the interaction of AMR pathogens between their hosts and the environment [23]. The majority of studies were either set exclusively in the community (n = 151, 55%) or in a healthcare facility (n = 74, 27%), with few (n = 11, 4%) exploring the link between these two (Table 1). Only eight studies (3%) modeled the transmission of AMR in long-term care facilities such as nursing homes, which are thought to be major reservoirs of AMR. The model populations were largely homogeneous and did not allow for variable mixing rates. A minority of the studies (n = 48, 18%) included heterogeneity in age, gender, sexual activity, and treatment status for pathogens such as TB, HIV, influenza, or malaria [24, 25]. Details can be found in Additional file 3: Table S4.

A large fraction of studies (n = 121, 44%) did not focus on a particular geographic area. Those that did were approximately evenly split between four regions: Africa (n = 35, 13%), the Americas (n = 36, 13%), Europe (n = 43, 16%), and Western Pacific (n = 24, 9%) (Fig. 4). Few studies modeled AMR in either the Eastern Mediterranean (n = 2, 1%) or South East Asian (n = 8, 3%) regions. Most models that did specify a geographic location focused on only one country and did not model transmission between countries. Five studies modeled global transmission of the pathogen of interest [26‐30]. There was an association between the pathogens modeled and country income status: 91% of studies (74/81) that specified locations and modeled HCAI were restricted to high-income countries (Table 2). On the other hand, the majority of TB and malaria modeling studies were set in low- and middle-income countries (LMIC) (Table 2). HIV was the only disease modeled across all regions (Table 2).

Of the 273 studies analyzed, most used deterministic models (n = 175, 66%). Other studies adopted stochastic models (n = 57, 22%), or hybrid deterministic models containing some elements of stochasticity (n = 7, 3%). A few studies compared the results of deterministic and stochastic methods (n = 25, 9.5%). Models were predominantly compartmental (n = 201, 76%) relative to individual-based models (n = 33, 12%). Several studies compared AMR outcomes using both model strategies (n = 7, 3%) (Table 1). A full breakdown of models by class is available in Additional file 1: Table S2.

Most studies considered more than one pathogen strain (n = 190, 72%), but the majority of the studies did not allow for co-infection of hosts, with a few exceptions (n = 22, 8%) (see Additional file 3: Table S4 for details). Half of the studies considered that the resistant strain carried a fitness cost (n = 132, 50%); however, fitness cost was often assumed, and few studies used primary data to infer this parameter (n = 21, 8%). With regard to the type of resistance studied, many models (n = 119, 45%) focused exclusively on transmitted resistance (secondary resistance) and significantly fewer models (n = 36, 14%) explored acquired or de novo resistance. Approximately a third of models (n = 89, n = 34%) accounted for both acquired and transmitted resistance, and some (n = 20, 8%) did not differentiate. Interestingly, a few studies integrated within- and between-host models (n = 17, 6%), allowing for joint exploration of emergence and transmission of AMR.

The accuracy of model results can also be assessed by out-of-sample validation techniques, in which model predictions are compared to independent observations that have not been used for model calibration. Only 36 studies (14%) reported out-of-sample model validation. From these, 31 used a statistical approach, while 5 simply conducted “face validity” tests by qualitative comparisons to empirical epidemiological datasets. There was no significant time trend in the type of models used, nor in the proportion of studies presenting a calibration or validation step (Additional file 1: Figure S4).

Mathematical models can be particularly useful to assess the effectiveness of intervention strategies (Table 3). Studies modeling interventions were approximately evenly split between interventions targeting non-resistant pathogens (n = 99) and those aimed specifically at suppressing resistance (n =100). Several articles (n = 17) explored interventions that could be classified as being aimed at the suppression of both susceptible and resistant pathogens. Of those aimed at reducing resistance (n = 117), few (n = 20) focused on reducing the emergence or acquisition of resistance, while the majority (n = 82) focused on the transmission of resistant pathogens, and some (n = 15) considered both (Table 3). Perhaps unsurprisingly, the majority of models (n = 85) focused on micro-level interventions affecting institutions (such as hospital-level interventions), with fewer (n = 32) focusing on macro-level interventions such as national policy changes or vaccines (Table 3).

We analyzed interventions based on the categories identified in a seminal report on AMR [18] (Table 3).The interventions studied were primarily improved hygiene or infection control measures (n = 59, 50%) such as hand hygiene, isolation, and decolonization. The impact of different drug regimens was often explored (n = 46, 39%) and included techniques such as mixing, switching, and cycling of drugs as well as changes to drug dosage and frequency. Surveillance of resistance (n = 32, 27%), rapid diagnostic techniques (n = 10, 9%), and a reduction in exposure to antimicrobials (n = 16, 14%) were also modeled. Relatively few studies included alternative treatment strategies or vaccines (n = 11, 9%). Only three studies modeled behavioral interventions (n = 3, 3%). Generally, many interventions modeled were organism specific, and further details can be found in Additional file 1: Table S3 and Additional file 3: Table S4.

We provide a short summary of the main findings of AMR modeling efforts for each of the top five diseases included in our review: MRSA, TB, HIV, influenza, and malaria.

Almost all of the 58 MRSA transmission studies focused exclusively on humans, except for three that explored MRSA in animals or the associations between animals and humans [22, 31, 32] (Table 1). The studies were mainly set in healthcare facilities (n = 49, 75%), with a few modeling transmission between hospitals and other settings (n = 5, 8%). Only one model was set in low-middle-income country. Key findings of these studies include: (1) reaffirming the importance of hand hygiene compliance; (2) the prediction of coexistence of community-acquired and hospital-acquired MRSA [33‐35], rather than the dominance of one over the other (although Webb et al. predict that community-acquired MRSA will dominate [36]); (3) the importance of effectively implementing appropriate screening, followed by isolation and/or decolonization; (4) the importance of hygiene and infectious disease control measures; and finally (5) two studies that proposed the intriguing concept of vaccines as a new weapon against MRSA [37, 38].

We identified a total of 43 models studying the dynamics of TB resistance in humans, mainly in community settings (n = 40, 93%). The studies modeled general transmission dynamics of multidrug-resistant (MDR) or extensively drug-resistant (XDR) TB and considered multiple interventions, most commonly intermittent preventative therapy (IPT); directly observed treatment, short-course (DOTS); and surveillance and drug susceptibility testing (Additional file 1: Table S3). Major conclusions include the following: (1) the vast majority of MDR-TB incidence is due to transmitted resistance rather than de novo treatment-related acquisition [30, 39, 40]; (2) to combat resistance, drug susceptibility testing and TB surveillance should be emphasized [41‐44]; (3) treatment and drug susceptibility testing should be expanded in community settings in Africa and the private sector in India [42, 43, 45‐47]; (4) controlling HIV would help decrease the transmission rates of resistant -TB [48, 49]; (5) isolation or quarantine strategies would help prevent transmission and decrease the number of patients lost to follow-up [50, 51]; and (6) while community-wide intermittent preventative therapy may increase the incidence of drug resistance, the benefits in reducing primary TB infections outweigh the risks. However, such therapy should be coupled with appropriate diagnostic and treatment policies [48, 52‐54].

HIV studies represented 13% of our data (n = 34). Topics modeled included the dynamics of HIV resistance in the context of the introduction of new pharmaceutical interventions (e.g., antiretroviral therapy, pre-exposure prophylaxis, vaginal microbicides, or structural interventions such as changes in diagnostics or treatment policy (Additional file 1: Table S3)). Seven additional papers modeled HIV-TB co-infection. Several manuscripts reached similar conclusions, most notably the following: (1) while oral pre-exposure prophylaxis is expected to reduce new HIV infections, a rise in de novo resistance is projected if prophylaxis is administered to those unknowingly infected with HIV [55‐62]; (2) similar findings apply to vaginal microbicides [63‐65]; and (3) modeling stresses the likelihood of accumulation of resistance over time as a response to various therapies and the importance of regular viral load testing and early diagnosis [66‐69]. Various changes in HIV treatment policy or diagnostics were also modeled [66, 68‐75].

Influenza resistance modeling studies (n = 30) mostly focused on humans, with few exceptions (one transmission model in chickens and one between ferrets) [76, 77]. Interventions modeled included use of antivirals (matrix ion channel or neuraminidase inhibitors), vaccines, antibiotics for treatment of secondary infections, and non-pharmaceutical interventions (isolation and social distancing) (Additional file 1: Table S3). Three repeating themes emerged: (1) there is support for the use of prophylactic drugs despite the risk of developing resistance during pandemic situations, but conditions varied [21, 78‐85]; (2) timing, dosage, and coverage levels of drugs are important when it comes to determining treatment effectiveness [82‐91]; and (3) there is a need for monitoring the transmissibility and/or fitness of the resistant virus [28, 77, 78, 92‐94].

A total of 22 studies described mathematical models for transmission of Plasmodium species in the context of AMR. All studies modeled Plasmodium falciparum in humans with the exception of one study of Plasmodium chabaudi in mice [95]. Geographically defined studies were restricted to Sub-Saharan Africa and the Thai-Cambodian region. Pharmaceutical interventions included the following drugs: artemisinin or artemisinin combination therapy (ACT), chloroquine, sulphadoxine, and pyrimethamine. Various non-pharmaceutical interventions were also modeled (Additional file 1: Table S3). Major conclusions include (1) the importance of using artemisinin as part of combination therapy regime (rather than monotherapy) [25, 96‐99] and (2) intermittent preventive therapy should be used carefully in areas where resistance is not already established [24, 100].