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Towards modeling phage therapy [1]

['Rob J. De Boer', 'Theoretical Biology', 'Bioinformatics', 'Department Of Biology', 'Utrecht University', 'Utrecht', 'The Netherlands', 'Santa Fe Institute', 'Santa Fe', 'New Mexico']

Date: 2026-06 

Patients infected with life-threatening multi-drug resistant (MDR) bacteria have been treated with cocktails of bacteriophages. This is a complicated form of personalized medicine as the phages given to a patient have to be selected beforehand on the basis of their lytic capacity of the infecting bacteria. Because bacteria rapidly become resistant, the evolution of resistance to a diverse cocktail of phages is a complicated dynamical process, during which competing bacterial strains replace one another by accumulating several resistance mechanisms, each of which may involve a fitness cost. As a consequence, it is typically not known why a particular phage therapy succeeded or failed, and how one can optimize the composition of the cocktails to maximize the rate of success. To improve upon this, we extend an existing in vivo-calibrated mouse model into a novel mathematical model for the human situation, and include multiple phages infecting multiple bacterial strains, differing in their resistance to each of the phages. We adjust several parameter estimates of the bacterial model to the human situation, and use the model to describe a successful case of phage therapy involving several cocktails, each containing several phages. In the model, treatment success crucially depended on pretreatment resistance levels, and on the diversity and the timing of the cocktails. Once an appropriate cocktail is found, it is less important to further optimize the infection rates of the phages. Resistant bacterial strains expand rapidly when sensitive strains decline, and the higher the infectivity of the phages, the faster resistant strains expand. Because resistance evolves rapidly, it is best to provide a diverse set of phages right from the start of therapy, i.e., to hit hard and early, and create a high genetic barrier to bacterial resistance.

Patients with dangerous antibiotic-resistant bacteria have been treated with mixtures of bacteriophages — viruses that infect bacteria. This treatment is highly personalized because the right phages must be selected for each patient’s infection. Since bacteria quickly evolve resistance to phages, it is often unclear why a treatment works or fails, and how to design the best phage combinations. To better understand this process, we developed a mathematical model of phage therapy in humans based on earlier mouse studies. The model includes multiple bacterial strains and multiple phages, each with different resistance patterns. We used the model to study a successful real-world phage therapy case involving several phage cocktails. The results show that treatment success depends strongly on the bacteria’s resistance before treatment, as well as on the diversity and timing of the phage cocktails. Since resistant bacteria rapidly take over once sensitive bacteria decline, the best strategy is to start treatment early with a broad and diverse phage cocktail to make it harder for bacteria to evolve resistance

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After developing a novel mathematical model having both thresholds, and allowing for several bacterial strains differing in their sensitivity to various phages and antibiotics, we illustrate its usefulness by describing a case of successful phage therapy of a patient suffering from a rampant infection with multi-drug resistant (MDR) Acinetobacter baumannii bacteria [ 3 , 4 , 17 ]. We present a few scenarios suggesting why this particular phage therapy might have been so successful. This patient was treated with several phage cocktails that were given sequentially, leading to rapid sequential development of bacterial resistance [ 7 ]. Most importantly, we find that the level of resistance increases rapidly when sensitive bacteria decline due to the (unsuccessful) phages in the first cocktail, and that this may markedly reduce the efficacy of subsequent cocktails. Thus, similar to lessons learned from treating rapidly evolving viruses like HIV, we find that it is important to ‘hit hard and early’ [ 18 ] by providing all phages at the same time, and to increase the ‘genetic barrier’ [ 19 ] by providing as many phages as possible.

Neutrophil densities rapidly increase during inflammation [ 14 ]. Because they are released more rapidly from the bone marrow, they can approach a new (higher) steady state level on a time scale of less than a day [ 15 , 16 ]. Thus, there should be two thresholds: (1) the maximum bacterial density that can be controlled by the normal density of neutrophils, e.g., small bacterial invasions that are controlled on a daily basis without triggering additional inflammation, and (2) the much higher threshold above which infections can grow uncontrolled despite the massive killing by neutrophils at their maximal density. In between an innate immune response is required to control the infection before it breaches the upper threshold.

The infection of bacteria by phages, and the rapid evolution of resistance by bacteria, has been studied extensively in vitro, and it is known that these systems tend to a approach an attractor where susceptible and resistant bacteria co-exist with the phages [ 8 , 9 ]. It was therefore surprising that phage therapy can be successful in vivo, and by elegantly combining modeling with experiments in mice, Roach et al. showed that the innate immune response, in this case mostly neutrophils, is largely responsible for the in vivo success of phage therapy in their experiments [ 10 , 9 ]. Apparently, neutrophils are usually incapable of controlling rampant bacterial infections, and a major effect of phage therapy is to reduce bacterial populations to a level where the killing of bacteria by neutrophils suffices to control bacterial growth. This mechanism requires the existence of a threshold in the bacterial density above which neutrophils can no longer control bacterial growth. Such a threshold is readily brought about in a model where at high bacterial densities (1) the neutrophils approach a maximum density, and (2) the number of bacteria killed per neutrophil per unit of time approaches a maximum, e.g., due to the fact that killing takes time [ 10 , 12 , 13 ].

Phage therapy may work for several reasons: (1) phages may simply infect and eliminate all bacteria (which is unlikely due to the rapid evolution of resistance [ 8 , 9 ]), (2) phages may reduce bacterial concentrations to levels where the host immune system regains control [ 10 ], (3) by evolving resistance to phages bacteria may regain sensitivity to particular antibiotics [ 2 , 4 , 5 , 11 ], (4) by modifying their capsule to prevent infection [ 7 ] bacteria may become more sensitive to killing by neutrophils, and (5) bacteria that evolved phage resistance may have such a crippled fitness that their replication rate drops below the rate at which the host immune system eliminates them. It seems virtually impossible to distinguish between these mechanisms on the basis of observational clinical data alone [ 1 , 6 ]. Because we expect many more people with multiple drug resistant (MDR) infections to be treated with phage therapy in the near future [ 2 ], we here develop mathematical models implementing these mechanisms, with the aim to employ these models for better interpretation of future data. Such models may help one optimize the design of therapy, and by fitting variations of these models to the data, one may become able to identify the mechanism(s) underlying the control of rampant bacterial infections by phage therapy in individual cases.

Due to the evolution of bacterial resistance to multiple types of antibiotics, viruses that can infect and kill bacteria (called bacteriophages), are receiving renewed interest as a treatment option for bacterial infections. Recent clinical successes with patients recovering from rampant bacterial infections due to personalized phage therapy, have sparked interest into the design, efficacy, and safety of cocktails of phages that can be given to patients [ 1 , 2 ]. Phage therapy has been used as ‘living antibiotics’ in the Soviet Union over extended periods of time [ 3 ], but these recent successes were ‘compassionate use’ cases of life threatening bacterial infections that were treated with personalized cocktails of phages hastily selected based on their capacity to lyse the bacteria causing the infection [ 4 – 7 ]. Unfortunately, the very limited host range of most bacteriophages calls for such a personalized approach, and is a major challenge for generalized treatments and clinical trials [ 1 ].

2 Results

The killing of bacteria by neutrophils has been studied widely in vitro [20–23] and in vivo [24,25]. Importantly, these data reveal that there are two types of thresholds, one for the neutrophils and one for the bacteria. The control of bacterial growth requires a minimum number of neutrophils, which has been called the critical neutrophil concentration (CNC) [20–22]. The in vitro data in these papers have been modeled successfully with exponential growth of bacteria, B, and mass-action killing by neutrophils, N, i.e., , revealing that the neutrophil density at which , i.e., , defines a CNC that is independent of the bacterial density [20–22]. Conversely, Drusano et al. [24,25] inoculated the thighs or lungs of mice with increasing doses of bacteria, and found a threshold in the initial bacterial density above which the infection grows uncontrolled (one could call this a critical bacterial concentration, CBC). A CBC is a natural outcome of a model in which the number of bacteria that can be killed by the maximum number of neutrophils approaches a maximum [12,13]. For instance, a model with a saturated killing rate, , in which a neutrophil can maximally kill kh bacteria per unit of time, has a CBC of . Since this saturation model approaches the mass-action model at low bacterial densities, i.e., when , this model also has a CNC at low bacterial densities. Malka et al. [23] vary both neutrophil and bacterial densities in ex vivo experiments, and find evidence for a double saturation model, , which also obeys mass-action kinetics at low densities, but decreases the killing rate per neutrophil as a function of the neutrophil density (for which there is additional evidence [26]). However, for reasons of simplicity, we here adhere to the conventional model in which the killing rate only saturates with the bacterial density.

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[1] Url: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1014408

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