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

Antibiotics are commonly regarded as one the greatest discoveries of the twentieth century; however, antibiotic or antimicrobial resistance (AMR) is now a significant threat to global health. According to a World Health Organization (WHO) global report [1], healthcare-acquired infections (HCAI) with AMR pathogens such as methicillin-resistant Staphyloccus aureus are a serious problem in high- and middle-income countries where surveillance is well established. There are also indications that the prevalence of HCAIs in low-income countries may be greater than in higher-income regions, although epidemiological data are scarce [1, 2]. In addition to the threat posed by HCAIs, low-income countries need to contend with the emergence of drug resistance to long-standing pathogens, namely human immunodeficiency virus (HIV), tuberculosis (TB), and Plasmodium parasites (malaria) [1].

There is an abundance and diversity of sources of drug pressure favoring the emergence of AMR (Fig. 1) [1, 3, 4]. Antimicrobials produced by pharmaceutical manufacturers are distributed widely across a diverse array of industries and applications. Unnecessary or suboptimal use of antimicrobials in humans and animals for medical or prophylactic purposes can promote AMR. Antimicrobial use in animals for growth promotion and intensive crop farming also facilitate evolution of AMR organisms, which can then enter the food chain. Other nonmedical uses of antimicrobials include industrial manufacturing (anti-fouling paint, detergents, ethanol production, food preservations, etc.). Solid or liquid waste contaminated with either AMR organisms or antimicrobials from these many sources may then enter municipal sewer systems or waterways. Thus, antimicrobial release from pharmaceutical manufacturers and non-pharmaceutical industries, combined with human and agricultural use, can lead to contamination of the soil and water [3, 4].

Once primary antimicrobial resistance arises in an organism, it can spread through numerous routes, both within hosts (e.g., via plasmids or mobile elements that are common in bacterial genomes) and between hosts, or via contaminated environment (Fig. 1). There are multiple recognized routes of transmission of AMR pathogens from agricultural farms to humans [5, 6]. Soil and water can also transmit AMR organisms to humans, animals, and plants. Aerosol or airborne transmission is common for respiratory pathogens that may carry resistance such as influenza or tuberculosis, while vectors can facilitate the spread of resistant malaria or bacteria, facilitating rapid diffusion over vast geographic areas [7, 8]. While AMR cannot be realistically eradicated, it may be possible to slow down or reduce its occurrence through antimicrobial stewardship, namely, strategies designed to improve the appropriate use of antimicrobials.

Mathematical models are increasingly used to help understand and control infectious diseases, particularly to identify key parameters driving disease spread, assess the effect of potential interventions, and forecast the trajectory of epidemics [9]. The most impactful modeling studies typically involve close feedback between modelers, public health experts, and clinicians, to identify an actionable research question, design and calibrate a model against empirical data, perform sensitivity analyses, refine the model as more data become available, and eventually issue policy guidance (Fig. 1). Modeling AMR organisms can be particularly challenging compared to modeling sensitive pathogens for several reasons (see Box 1). In addition to crucial data gaps, modelers have to contend with issues of pathogen heterogeneity, fitness costs, co-infections, and competition, which are important features of resistance that remain poorly understood and quantified.

The contribution of mathematical modeling to the control of emerging infections is well established [9], and mathematical modeling can also be a powerful tool to guide policies to control AMR. Here, we undertake a systematic review to assess how population-level mathematical and computational modeling has been applied in the field of AMR over a period of 11 years (2006–2016). Previous reviews of AMR modeling were either completed some time ago [10, 11], only applied to a specific subset of AMR, such as HCAIs [12, 13], or focused on acquired resistance [14]. Our goals in this study were to (1) identify the predominant pathogens, populations, and interventions studied; (2) highlight recent advances in the field; (3) assess the influence of the research; and (4) identify gaps in both modeling of AMR and data availability.

Details of the screening process can be found in the PRISMA diagram in Fig. 2. A total of 2466 articles were identified after removing duplicates. Two rounds of title and abstract screening removed a further 2143 records. A total of 323 articles were earmarked for full-text review. Upon reading these, we found that 50 articles did not meet the inclusion criteria specified above, which resulted in a final tally of 273 records included in our analyses. We describe the characteristics of all studies below and then focus on key findings for the five pathogens or diseases most commonly modeled: methicillin-resistant Staphylococcus aureus (MRSA), tuberculosis (TB), human immunodeficiency virus (HIV), influenza, and malaria.

Trends in the number of published modeling studies

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).

Host and population settings used in AMR modeling

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.

	TOTAL	MRSA	TB	HIV	Influenza	Malaria
Host type	(n = 273)	(n = 65)	(n = 43)	(n = 34)	(n = 30)	(n = 22)
Human	233 (89%)	62 (95%)	43 (100%)	34 (100%)	28 (93%)	21 (95%)
Animal	18 (7%)	2 (3%)	–	–	2 (7%)	1 (5%)
Human-animal	7 (2%)	1 (2%)	–	–	–	–
Plant	5 (2%)	–	–	–	–	–
Population type
Community (endemic)	154 (58%)	7 (11%)	40 (93%)	34 (100%)	25 (83%)	21 (95%)
Healthcare facility	71 (27%)	49 (75%)	1 (2%)	–	–	–
Community-healthcare facility	11 (4%)	5 (8%)	2 (5%)	–	1 (3.5%)	–
Agricultural-farming	20 (8%)	1 (1.5%)	–	–	1 (3.5%)	–
Other	8 (3%)	3 (4.5%)	–	–	3(10%)	1 (5%)
Model parameters
Referenced data	191 (72%)	34 (52%)	38 (88%)	32 (94%)	29 (97%)	17 (77%)
Primary data	73 (28%)	31 (48%)	5 (12%)	2 (6%)	1 (3%)	5 (23%)
Model type
Deterministic	175 (66%)	30 (46%)	36 (84%)	23 (70%)	18 (60%)	18 (82%)
Stochastic	57 (22%)	30 (46%)	6 (14%)	5 (12%)	3 (10%)	2 (9%)
Both (D and S)	25 (9%)	5 (8%)	1 (2%)	4 (12%)	8 (27%)	1 (5%)
Hybrid	7 (3%)	–	–	2 (6%)	1 (3%)	1 (5%)
Model class
Compartmental	201 (76%)	34 (52%)	37 (86%)	27 (79%)	26 (87%)	19 (86%)
Individual-based	33 (12%)	19 (29%)	3 (7%)	4 (12%)	1 (3%)	1 (5%)
Both	7 (3%)	1 (2%)	–	2 (6%)	1 (3%)	1 (5%)
Other	23 (9%)	11 (17%)	3 (7%)	1 (3%)	2 (7%)	1 (5%)
Model features
Multi-strain model	190 (72%)	23 (35%)	42 (98%)	32 (94%)	29 (97%)	17 (77%)
Co-infection of hosts	22 (8%)	5 (8%)	9 (21%)	5 (15%)	3 (10%)	3 (14%)
Fitness cost modeled	132 (50%)	15 (23%)	32 (74%)	20 (59%)	25 (83%)	13 (59%)
Acquired and transmitted resistance	89 (34%)	1 (2%)	26 (60%)	28 (82%)	20 (67%)	5 (23%)
Within-host model	17 (6%)	1 (2%)	3 (7%)	2 (6%)	1 (3%)	4 (18%)
Population stratification	48 (18%)	4 (6%)	11 (26)	18 (53%)	3 (10%)	4 (18%)
Model rigor
Calibration	115 (43%)	33 (51%)	26 (60%)	16 (47%)	4 (13%)	3 (14%)
Validation	36 (14%)	10 (15%)	11 (26%)	5 (15%)	0 (0%)	1 (5%)
Sensitivity analyses	159 (60%)	36 (55%)	32 (74%)	25 (74%)	16 (53%)	14 (64%)
Economics
Cost/benefit analysis	23 (9%)	8 (12%)	6 (14%)	6 (18%)	1 (3%)	3 (14%)

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).

Infectious disease system	Total	High	Upper-middle	Low-middle	Low	ND
MRSA	65	38	2	1		24
TB	43	3	15	7		25
HIV	34	4	9	4	2	15
Influenza	30	5				25
Plasmodium falciparum	21		1	5	1	14
General bacteria	17	4				13
Streptococcus pneumoniae	12	6			1	5
Enterococci (VRE)	10	7				3
Escherichia coli	9	6	1			2
Neisseria gonorrhoeae	6	3				3
Acinetobacter baumannii	4	1	1			2
Zymoseptoria tritici	4	3				1
Enterobacteriaceae (ESBL-E)	3	2				1
Klebsiella pneumoniae	3	3
Teladorsagia circumcincta	3	3
Campylobacter	2	2
General protozoan	2	1				1
Nematodes	2	1				1
Pseudomonas aeruginosa	2	2
Salmonella spp.	2	1			1
Schistosoma mansoni	2					2
Blumeria graminis	1	1
Enterobacteriaceae, CRE	1		1
Leishmania donovani	1			1
NS	1					1
Plasmodium chabaudii	1					1
Shigella spp.	1	1
Trichostrongylus colubriformis	1	1
Wucheria bancrofti	1				1

A representation of pathogens modeled by the World Bank income level classification: high, upper-middle, low-middle, low, or not described (ND).

Our systematic review of transmission modeling of AMR over a decade highlights a continuous increase in publications during 1996–2012, a peak in 2013 (n = 38), and a plateau in the following 3 years (average annual publications = 25). Modeling of AMR overall experiences a slower progression than a related field such as individual-based infectious disease models. Five infectious diseases have dominated mathematical models of AMR during 2006–2016: MRSA, TB, HIV, influenza, and malaria. The majority of AMR articles focused exclusively on humans, either in community or healthcare settings, rather than modeled interactions between hosts or multiple settings. Over the study period, a majority of models remained data-free and few were validated against independent datasets. Many models assumed a fitness cost for resistant organisms; however, this was often not derived from primary experimental or epidemiological data. Few models integrated within-host dynamics or economic factors into their transmission framework. Most of the interventions aimed at combating AMR were primarily focused on transmitted rather than acquired resistance and were implemented on a micro-level scale. The interventions considered the impact of different drug regimens, hygiene and infection control measures, or screening and diagnostics, while less than 5% addressed alternative therapeutic strategies or behavioral changes.

The predominance of five pathogens in AMR transmission modeling is likely driven by a long history of disease modeling for at least four of these pathogens (TB, HIV, influenza, and malaria) and an early recognition of MRSA as an important drug-resistant pathogen, combined with availability of epidemiological and surveillance data. Historically, these diseases have taken a large toll on global morbidity and mortality rates; however, it has been predicted that the consequences of AMR in other pathogens may rapidly outpace them by 2050 [18]. More research should be undertaken before resistance in other disease systems becomes a major crisis.

Other serious threats based on WHO or CDC criteria that are rarely modeled include Campylobacter (n = 2), Salmonellae spp. (n = 2), Neisseria gonorrhoeae, and Shigella spp. (n = 1). Importantly, we were unable to find any published AMR models for the following serious threats: Helicobacter pylori, Haemophilus influenzae, fluconazole-resistant Candida, clindamycin-resistant group B strep, and erythromycin-resistant group A strep. While mathematical transmission models do exist for wild-type H. pylori [102], H. influenzae [103], and Candida parapsilosis [104], we are not aware of any models for resistant strains, which may have different transmission parameters than susceptible strains.

Most models did not consider pathogen heterogeneity, such as multiple viral or bacterial strains, parasite species, or multiple resistance mechanisms (e.g., membrane permeability, enzymatic degradation, mutation of antimicrobial targets), which might affect transmission potential. As a case in point, most malaria modeling has dealt with the Plasmodium falciparum species in Africa or East Asia. This is presumably based on the long-held assumption that the majority of malaria burden is caused by P. falciparum rather than other plasmodium species. However, there is growing evidence that Plasmodium vivax, which is endemic in South and South-East Asia as well as Central and South America, is associated with a significant burden of morbidity and associated mortality [105, 106]. P. vivax is already largely resistant to chloroquine [107], though resistance to artemisinin has not yet been reported. A similar issue exists in regard to mathematical modeling studies of HIV, where no distinction was made between HIV-1 and HIV-2, which are known to have markedly different resistance profiles to the various antiretroviral drugs used [108, 109]. This is likely because HIV-2 has historically infected a much smaller, but significant, proportion of the population. It was estimated in 2006 that one to two million people [110] in several West African countries were infected with HIV-2, though we could not find more recent estimates.

While there has been increasing effort to design models with explicit interactions between community and hospital populations, few include long-term care facilities, which often lack effective antimicrobial stewardship programs [111–113]. Most worrisome perhaps, almost all models were set in humans and there were few attempts to tackle the hypothesized connection between veterinary/agricultural use of antibiotics and AMR. No studies modeled AMR transmission in aquaculture, despite the growing body of evidence that AMR resistance could enter the food chain through these means [114, 115]. Similarly, there were few ecological studies on the transmission of AMR from the environment (water, soil, etc.) to potential hosts, despite the increasing evidence for a link between antimicrobial contamination of the environment, and the development and transfer of resistance to human pathogens [116–118]. This is particularly concerning given the large quantity of antibiotics used in agricultural facilities, the lack of regulation on their waste disposal and the inability of many sanitation systems to filter out antimicrobials and AMR elements. Another environmental factor that was not modeled was the effect of climate change on the rates of AMR. Recent research has shown that increasing temperatures are associated with increased levels of resistance [119, 120], but there is no projection of AMR patterns under climate change scenarios.

We found that the vast majority of HCAI and influenza models were set in high-income countries, although this is an increasingly recognized threat in LMIC [1]. The lack of studies in developing countries is particularly concerning because of unregulated or poorly regulated antimicrobial manufacturing and usage [121, 122]. This is likely due to lack of appropriate diagnostics and surveillance in low-resource settings [1, 122].

A major reason for the lack of modeling studies on particular pathogens or certain settings is likely to be a deficiency in available data needed for model calibration and design. There is a need for more precise data on antibiotic consumption rates in both humans and animals [18], which is often not made publicly available [123–125]. In addition, improved surveillance of AMR incidence is required in humans, animals, and the environment (soil and water) [126]. There have been several examples of zoonotic transmission of AMR in both domestic [127, 128] and wild animals [129, 130] as well as evidence of transmission of genetic determinants of AMR into the environment [3, 116], which in turn may facilitate further dissemination of resistance.

In terms of AMR-specific model dynamics, half of the reviewed studies factored in a fitness cost for the resistant strain; however, this was often assumed and rarely estimated from primary data. Additionally, many models did not distinguish between acquired (de novo) or transmitted resistance. This is important for accurately defining model parameters such as reversion [131] or transmission rates [78, 132], which ultimately affect model outcomes. Most studies modeled homogeneous infections with a single pathogen strain and therefore did not investigate host co-infection and strain competition. Host populations were also largely assumed to be mixing homogeneously with no stratification by age, susceptibility, or contact patterns. Integration of within- and between-host models was also rare; multi-scale modeling is an important frontier for AMR and more broadly for the field of infectious disease modeling [133].

Previous reviews predicted that technological advances in computational tools could allow for more complex models and calibration to larger datasets [9, 13]. Consistent with this prediction, a sharp increase was reported in the field of individual-based models of infectious diseases, but this increase has not percolated to the field of AMR [16]. The majority of AMR transmission models reviewed here remain theoretical, with little attempt to compare model predictions to epidemiological data, and calibration with independent data is scarce. It should also be noted that improvements could also be made in terms of documenting modeling methods. Only 47% of the studies assessed cited the modeling software or computational tools used and few described modeling techniques in a way that might be able to be reproduced by researchers who are not already experienced modelers. Even fewer manuscripts provided the computational code used: two manuscripts provided a link (both were expired at the time of this writing), and three were willing to share the code upon request. Some attempts have been made to standardize the terminology, methodology, and reporting structure for infectious disease transmission models [134–136], but better documentation of modeling methods is needed for reproducibility. Furthermore, it would also be useful to make the underlying AMR epidemiological datasets publicly available to aid reproducibility.

With regard to interventions aimed at combating AMR, many models incorporated elements of improved hygiene or infection control in order to combat the spread of AMR. No model focused on “macro” scale interventions such as improved access to water and sanitation facilities that can curb the transmission and development of resistance. Improved water, sanitation, and hygiene can lead to a decrease in respiratory and diarrheal disease, both of which are often unnecessarily treated with antibiotics although the causative agents may be viral [137, 138]. Numerous interventions examined improved surveillance or diagnostic methods, particularly for HIV and TB, but were lacking for many bacterial diseases outside of healthcare settings. Many diagnostic methods for antimicrobial resistance are culture based, and confirmation of resistance, let alone specific genotyping, may take several days. There is an urgent need for rapid molecular diagnostics in order to improve antimicrobial stewardship; more modeling work in this area could highlight the transmission and cost-effectiveness benefits of such technologies.

Surprisingly, few studies modeled reduction in the use of antimicrobials as an intervention, particularly when supplied to food animals either as a growth supplement or prophylaxis. Several models studied the effects of reducing antimicrobial exposure levels in healthcare settings [139–142], but there were fewer for animals [143–145]. No models for AMR or AMR-related interventions in aquaculture settings exist.

Many infectious disease models increasingly incorporate features of human behavior [123–125, 146]; however, this is not common in the field of AMR modeling outside of healthcare facilities. In addition, most models did not consider how social, cultural, or behavioral differences might affect resistance development or transmission. Those that did were mainly focused on sexually transmitted infections such as HIV or N. gonorrhoeae. Similarly, few models included vaccination despite increasing appreciation for the role they could play in reducing antimicrobial consumption [147, 148]. Vaccines can also have indirect effects on antimicrobial consumption [147, 148] by reducing the number of pharmaceuticals erroneously prescribed for viral infections. Several vaccine candidates are under development for C. difficile, S. aureus, group B Streptococcus, E. coli, and respiratory syncytial virus [149]; mathematical models could be used to evaluate their potential effects at a population level and inform cost-effectiveness analyses.

The increasing availability of multiple epidemiological and pathogen genetic data streams offers exciting new possibilities to improve and expand modeling capabilities. Enhanced access to, and integration of, digital disease surveillance data [150] into epidemiological analyses could help further strengthen model validation. Pathogen genomic sequences (together with relevant metadata such as date, location) can also inform many aspects of transmission dynamics. And although some have started integrating genomic data [151] into modeling studies, this is the exception rather than the norm in the field of AMR. An integrative approach will be required to synthesize large amounts of data together, which will ideally help to develop more realistic AMR models tailored to specific populations. It is noteworthy that few publications addressed the spatial diffusion of AMR; a lack of spatially resolved AMR datasets may explain this gap.

This review has some limitations. We have only searched four databases most relevant to biomedical sciences. Furthermore, in an effort to keep the amount of search results to a manageable number, we use certain keywords specific to population dynamic studies of AMR organisms. Therefore, we may have inadvertently excluded some publications (without these keywords) relevant to this review. However, we are confident that this review provides an accurate overview of overall trends in the field.

The field of AMR modeling is growing but is limited by both the quantity and quality of available data. Success stories include accurate predictions of the emergence of resistance in malaria [152], MDR-TB [153], and influenza [154], and modeling is also frequently used to inform AMR stewardship programs in healthcare facilities [155]. Our review suggests a need for more applied, data-driven models, better tuned to and diversified to reflect the public health concerns highlighted by the WHO and the CDC. Although the overall increase in AMR transmission modeling in the last decade is encouraging, the recent plateau in published work and scarcity of studies on high-concern pathogens should be addressed. Most importantly perhaps, more forward-thinking models should be developed to predict the emergence of resistance in pathogens where the issue is not yet rampant and evaluate how policy and behavioral changes can curb drug pressure and mitigate AMR. Research programs in support of AMR modeling, increased data collection efforts, and stronger links between modelers and public health experts are warranted to stimulate this field.