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Antibiotic Treatment, Duration of Infectiousness, and Disease Transmission J Environ Sci Public Health 2021;5 (2):251-272 DOI: 10.26502/jesph.96120128 Research Article Antibiotic Treatment, Duration of Infectiousness, and Disease Transmission Thomas Caraco* Department of Biological Sciences, University at Albany, Albany, NY, 12222, USA *Corresponding Author: Thomas Caraco, Department of Biological Sciences, University at Albany, Albany, NY, 12222, USA Received: 12 March 2021; Accepted: 22 March 2021; Published: 08 April 2021 Citation: Thomas Caraco. Antibiotic Treatment, Duration of Infectiousness, and Disease Transmission. Journal of Environmental Science and Public Health 5 (2021): 251-272. Abstract infectious host's time-dependent probability of By curing infectious individuals, antibiotic therapy pathogen transmission, as well as the probabilistic must sometimes limit the spread of contagious disease duration of the infectious period. among hosts. But suppose that a diseased host stops transmitting infection due either to antibiotic cure or At the within-host scale, the model varies (1) to non-therapeutic removal (e.g., isolation or inoculum size, (2) bacterial self-regulation, (3) the mortality). An antibiotic`s suppression of within-host time between infection and initiation of therapy, and pathogen growth increases the likelihood of curing a (4) antibiotic efficacy. At the between-host scale the single infection and may also reduce the probability model varies (5) the size of groups randomly of non-therapeutic removal. If antibiotic treatment encountered in the infectious host’s environment. relaxes the total rate of infection removal sufficiently to extend the average duration of infectiousness, Results identify conditions where an antibiotic can between-host transmission can increase. That is, increase duration of a host`s infectiousness, and under some conditions, curing individuals with consequently increase the expected number of new antibiotics can impact public health negatively (more infections. At lower antibiotic efficacy, therapy might new infections). To explore this counter-intuitive, but convert a rare, serious bacterial disease into a plausible effect, this paper assumes that a common, but treatable infection. deterministic within-host dynamics drives the Journal of Environmental Science and Public Health 251 J Environ Sci Public Health 2021;5 (2):251-272 DOI: 10.26502/jesph.96120128 Keywords: Group size; Infectious contacts; antibiotics increase host survival. Therapeutic Inoculum; Isolation; Pathogen extinction; Within-host recovery of a treated individual may imply a public- dynamics health benefit. If antibiotics shorten the infectious period, the count of infections per infection could 1. Introduction decline [4]. This interpretation follows from SIR Antibiotics are administered routinely to humans, compartment models, where neither the host-removal agricultural/pet animals, and certain plants [1-3]. rate nor the antibiotically-induced recovery rate Most commonly, antibiotic treatment is intended to depends explicitly on within-host pathogen density. control an individual`s bacterial infection [4]. Beyond That is, antibiotics are assumed to reduce duration of concerns about the evolution of resistance [5, 6], use the infectious period and to exert no effect on per- of antibiotics to treat infection presents challenging individual transmission intensity. By extension, questions, including optimizing trade-offs between antibiotics may then reduce pathogen transmission. antibacterial efficacy and toxicity to the treated host [7]. This study asks if antibiotic treatment of an However, antibiotic therapy might, in other cases, infection can have untoward consequences at the increase the expected length of the infectious period. population scale; the paper models an antibiotic's Transitions in host status must often depend on a direct impact on within-host pathogen dynamics and within-host dynamics [8, 11]. As infection progresses, resulting, indirect effects on between-host the pathogen density's trajectory should drive change transmission [8, 9]. in the rate of host removal while ill (e.g., isolation), the rate of recovery from disease, as well as the rate at The model assumes that the antibiotic`s suppression which infection is transmitted [12, 13]. For many of within-host bacterial density extends the average human bacterial infections, an individual can still waiting time for the host`s removal from transmit the pathogen after beginning antibiotic infectiousness via other processes (e.g., physical therapy [14]. Common infections remain isolation or disease mortality). The paper`s focal transmissible for a few days to two weeks [15]. question asks how varying the age of infection when Although not addressed here, sexually transmitted antibiotic treatment begins impacts both the duration disease may persist within a host for months after of disease and the intensity of transmission during the antibiotic therapy has begun [16]. Therapeutic host`s infectious period. When removal equates with reduction in pathogen density might eventually cure disease mortality, the results identify conditions under the host, while allowing the host to avoid isolation, which an antibiotic may simultaneously increase both etc. during treatment [17]. The result might be a survival of an infected individual and the expected longer period of infectious contacts and, number of secondary infections. consequently, increased secondary infections. 1.1 The infectious period This paper assumes that with or without antibiotic Efficacious antibiotics, by definition, reduce within- treatment, a diseased host`s infectious period may be host pathogen density [10]; for some infections, ended by a removal process that depends on within- Journal of Environmental Science and Public Health 252 J Environ Sci Public Health 2021;5 (2):251-272 DOI: 10.26502/jesph.96120128 host pathogen density. As a convenience, removal probabilistically [27-29]. At the within-host scale, the includes any event terminating infectious contacts model considers both density-independent and self- with susceptible hosts, prior to the antibiotic curing regulated pathogen growth. The host`s removal rate the disease. Social/physical isolation [18] and host and the infection-transmission intensity will depend mortality are dynamically equivalent removals in that directly on the time-dependent bacterial density. they end the infectious period. The model assumes Pathogen density increases monotonically from time that an antibiotic, by deterring within-host pathogen of infection until antibiotic treatment begins, given growth, increases the expected waiting time for persistence of the host`s infectious state. The removal, but an increase in antibiotic efficacy reduces antibiotic then reduces pathogen density until the host the time elapsing until the host is cured. This is cured or removed prior to completing therapy interaction affects the count of secondary infections; (whichever occurs first). disease reproduction numbers (before and after therapy begins) identify conditions where an Counts of secondary infections will require the antibiotic increases the spread of disease. temporal distribution of infectious contacts, since the transmission probability depends on the time- 1.2 Random encounters: susceptible groups dependent pathogen density [13, 30]. The results When infection is rare, random variation in the explore effects of antibiotics and inoculum size [31] number of contacts between diseased and susceptible on length of the infectious period, disease hosts influences whether the pathogen does or does reproduction numbers, and pathogen extinction. The not spread at the population scale [19, 20]. Therefore, last two results connect logically; the first addresses this paper treats reproduction numbers, i.e., infections mean infections per infection, and the second per infection, as random variables [21]. The concerns the variance in the count of new infections. environment governs social group size, which can affect contacts between infectious and susceptible 2. Within-Host Dynamics: Timing of hosts, and so impact infection transmission [22-24]. Antibiotic Treatment The model asks how the number of hosts per For many bacterial infections of vertebrates, little is encounter with an infectious individual (with the known about within-host pathogen growth [32]. In the product of encounter rate and group size fixed) laboratory, Pseudomonas aeruginosa readily infects impacts the variance in the count of secondary Drosophila melanogaster [33]; the pathogen increases infections; specifically, the paper asks how group size exponentially until the host dies or antibacterial impacts the probability that a rare infection fails to treatment begins [29, 34, 35]. In more complex host- invade a host population [25, 26]. pathogen systems, resource limitation or physical crowding must often decelerate pathogen growth 1.3 Organization within the host, implying self-regulation [36-39]. The model treats within-host pathogen dynamics Numerical results below compare ways in which the deterministically [2]. Removal from the infectious strength of self-regulation interacts with an antibiotic state and between-host transmission are modeled Journal of Environmental Science and Public Health 253 J Environ Sci Public Health 2021;5 (2):251-272 DOI: 10.26502/jesph.96120128 to influence duration of infectiousness, and intensity replication and mortality rates per unit density. The of pathogen transmission. latter rate may reflect a nonspecific host immune response
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