Modeling the role of bacteriophage in the control of cholera outbreaks Mark A. Jensen*, Shah M. Faruque���, John J. Mekalanos�����, and Bruce R. Levin* *Department of Biology, Emory University, Atlanta, GA 30332 ���Molecular Genetics Laboratory, International Centre for Diarrhoeal Disease Research Bangladesh, Dhaka-1212, Bangladesh and ���Department of Microbiology and Molecular Genetics, Harvard Medical School, Boston, MA 02115 Contributed by John J. Mekalanos, January 7, 2006 Cholera is a waterborne diarrheal disease that continues to plague the developing world. Individuals become infected by consuming water from reservoirs contaminated by virulent strains of the bacterium Vibrio cholerae. Epidemiological and environmental ob- servations of a cholera outbreak in Dhaka, Bangladesh, suggest that lytic bacteriophage specific for V. cholerae may limit the severity of cholera outbreaks by killing bacteria present in the reservoir and in infected individuals. To quantify this idea and generate testable hypotheses, we analyzed a mathematical model that combines the epidemiology of cholera with the population dynamics of the bacteria and phage. Under biologically reasonable conditions, we found that vibriophage can ameliorate cholera outbreaks. If phage predation limits bacterial density before an outbreak, a transient reduction in phage density can disrupt that limitation, and subsequent bacterial growth can initiate a cholera outbreak. The severity of the outbreak depends on the density of phage remaining in the reservoir. If the outbreak is initiated instead by a rise in bacterial density, the introduction of phage can reduce the severity of the outbreak and promote its decline. In both situations, the magnitude of the phage effect depends mainly on vibrio growth and phage mortality rates the lower the rates, the greater the effect. Our analysis also suggests that either bacteria in the environmental reservoir are hyperinfectious or most victims ingest bacteria amplified in food or drinking water contami- nated by environmental water carrying few viable V. cholerae. Our theoretical results make a number of empirically testable predictions. Vibrio cholerae epidemiology Cicant holera, a waterborne gastroenteric infection, remains a signif- threat to public health in the developing world. The disease in its severest form causes copious diarrhea lasting from 3 to 7 days. Death from dehydration is typical in the absence of treatment. Pathogenic serotypes of the bacterium Vibrio cholerae, expressing cholera toxin encoded by a lysogenic bacteriophage (1), are responsible for the majority of cases. V. cholerae and other members of this bacterial genus naturally colonize lakes, rivers, and estuaries (2, 3) local outbreaks are precipitated and prolonged by contamination of local water supplies in areas of poor sanitation. Disease transmission usually occurs through ingestion of contam- inated water or feces rather than through casual human���human contact. Outbreaks of cholera occur cyclically, usually twice per year in endemic areas, and the intensity of these outbreaks varies over longer periods. Extrinsic factors, such as large-scale weather cycles (e.g., the El Nin ��o���Southern Oscillation), and intrinsic factors such as postinfection immune periods have been shown to correlate in time with components of the epidemic cycle (4���6). Recently, Faruque et al. (7) proposed that lytic bacteriophage predation on pathogenic vibrio may be an important extrinsic factor influencing the epidemic cycle on short time scales and may act to modify the duration and severity of cholera outbreaks. In support of this interpretation, they reported longitudinal observations of cholera cases and environmental vibrio and phage densities during a local cholera outbreak in Dhaka, Bangladesh (Fig. 1). These data in- cluded cholera incidence, concentrations of the responsible V. cholerae strain (streptomycin-resistant O1 serotype), and a strain- specific lytic phage (JSF4) in the stool of hospitalized patients and in nearby water bodies. Their study was unique, in that the outbreak could be attributed to a single V. cholerae clone, the density of which could be readily monitored in the environment by its resistance to streptomycin. Disease incidence (inferred from hospitalizations) and reservoir bacterial concentrations rose and fell together. The density of JSF4 phage in the reservoir and the patient also waxed and waned with the outbreak. On the basis of these population dynamic observations, Faruque et al. (7) suggested that infections are caused by ingestion of vibrio deriving from a common reservoir, in which bacteria and phage also reproduce and interact independently of the human population. First, transient environmental conditions set the stage for both a reduction of phage and a bloom of vibrio in the reservoir. As a consequence of the increase in the density of virulent V. cholerae in the reservoir, humans become infected and begin to shed increasing numbers of bacteria into the reservoir, further elevating bacterial density and exacerbating the outbreak. Next, phage production is renewedinthereservoir.Phagereplicateontheincreasingnumbers of bacteria in both the reservoir and infected individuals. Decline in bacterial density ultimately results from increasing phage pre- dation, returning reservoir bacterial populations to pre-outbreak levels and ending the outbreak. The rate of reduction of bacterial density presumably is faster than it would be if the reduction were solely the consequence of the decline in the numbers of susceptible individuals. Faruque et al. (7) stress the assumption that large numbers of phage might be generated within infected individuals and shed into the reservoir, and that this ������amplification������ may be critical component of phage-modulated cholera epidemics. Although the observed changes in bacterial and phage densities are qualitatively consistent with this hypothesis, these dynamics may also be incidental to the epidemic process. For example, the decline in bacterial concentration could be entirely due to immune- mediated recovery or death of infected individuals. The consequent reduction of bacteria numbers in the effluent might fully account for the decline in disease incidence and density of phage preying on these bacteria. In this interpretation, the outbreak drives the changes in phage populations, rather than the reverse. In an effort to evaluate the potential importance of phage predation to the epidemic course of cholera, we have developed a mathematicalmodelincorporatingboththepopulationdynamicsof the bacteria and phage and the epidemiology of cholera (Fig. 2). Our model is based on the conceptual model presented in ref. 7 and extends and modifies existing models of the epidemiology of cholera (8, 9) to allow interaction between populations of bacteria and phage. We explore the conditions under which phage can impact the epidemic course. In our numerical analysis of the properties of this model, we give particular consideration to the parameter conditions under which the data obtained in the studies Conflict of interest statement: No conflicts declared. ��To whom correspondence should be addressed. E-mail: jmekalanos@hms.harvard.edu. �� 2006 by The National Academy of Sciences of the USA 4652���4657 PNAS March 21, 2006 vol. 103 no. 12 www.pnas.org cgi doi 10.1073 pnas.0600166103

of Faruque et al. (7) can be recovered and are consistent with those estimated for the interactions between bacteria and phage. We discuss the implications of our theoretical analysis for empirical tests of hypotheses about the role of lytic phage in the cyclic behavior of cholera outbreaks. Results Bacteria-Phage Dynamics: Resource vs. Phage Control. If the bacteria have a positive net growth rate (m 0) in the reservoir, there are three equilibrium states for the bacteria and phage populations (see Supporting Text, which is published as supporting information on the PNAS web site, for details). The first, where bacteria and phage densities are both zero, is always unstable. That is, the system will drive small increases in both bacteria and phage densities to one of the other equilibria, for which either (i) only bacteria persist, or (ii) bacteria and phage coexist. Stability of these equilibria depends on the composite parameter Kv . Oneinterpretationof isasthebasicreproductivenumberofthe phage ������epidemic������ in the bacterial population a single infected cell introduced to a naive equilibrium population will be responsible for new ������infections.������ If 1, bacterial densities tend to the carrying capacity Kv, and phage densities decay to zero. We will refer to this situation as ������resource control.������ If 1, bacterial density tends to Kv Kv, and phage density tends to a nonzero equilibrium, coexisting with the bacteria. We refer to this as ������phage control.������ The conceptual model (7) supposes a preexisting balance be- tween bacteria and phage, upset by a transient loss of phage at the start of an epidemic. In our treatment, this is equivalent to an outbreak induced by phage instability, in the context of phage control ( 1). We also considered resource control ( 1) and asked to what extent introduced phage would ameliorate an epi- demic induced by a bacterial bloom. Below, we show that the two situations result in different outbreak dynamics. Resource Control: Bloom-Induced Outbreaks. We consider an exam- ple of bloom-induced outbreak dynamics in Fig. 3, with phage present and absent. Bacterial density quickly drops to carrying capacityinbothcases,butthepresenceofphagespeedsthisprocess, reducing the peak and duration of the outbreak. Phage densities peak within a couple of days, and microbial densities return to equilibrium by 2 weeks. These dynamics are much faster than those reported for reservoir densities in the Dhaka outbreak (7). For this example, we chose 2 3, which implies a carrying capacity Kv 2.5 106 3.8 107 cells per liter over the experimental range of the phage decay rate . The magnitude of the epidemic, as measured by the number of cases above the expected endemic number (the ������excess cases������), is Fig. 1. Epidemic and microorganism data from ref. 7. (A) Environmental bacterial density index and phage densities. (B) Numbers of hospitalized cholera patients. (C) Estimated proportion of phage-positive infected patients. Lines are less-smoothed fits (24) to the data, provided for visual convenience. Fig. 2. Flow diagram for cholera and phage model. Compartments: S, susceptible individuals I , infected with V. cholerae I , infected with V. cholerae and phage R, recovered dead V, reservoir bacterial density P, reservoir phage density. See text for detailed description and Table 1 for parameter definitions. Fig.3. Epidemiccurves,withandwithoutphage,forbloom-inducedepidemics. y axis, number of disease cases x axis, time in weeks solid line, no phage present dottedline,phage-moderatedepidemic,initialphagedensity106 virionsperliter. (Inset) Bacteria and phage density over time. Other parameters: initial bacterial density, 5 Kv (Kv 2.5 106 cells per liter), m 0.3, 0.525, k 4 107, l 2.1 107, 1, 0.1, 0.1, 0.67, 10 4, a 7. Jensen et al. PNAS March 21, 2006 vol. 103 no. 12 4653 MICROBIOLOGY