Modeling the role of bacteriophage in the control of cholera outbreaks

Abstract

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 observations 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 contaminated by environmental water carrying few viable V. cholerae. Our theoretical results make a number of empirically testable predictions.

Fig. 1.

Epidemic and microorganism data from ref. . (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.

Epidemic curves, with and without phage, for bloom-induced epidemics. y axis, number of disease cases; x axis, time in weeks; solid line, no phage present; dotted line, phage-moderated epidemic, initial phage density 10⁶ virions per liter. (Inset) Bacteria and phage density over time. Other parameters: initial bacterial density, 5 × K_v (K_v = 2.5 × 10⁶ cells per liter), m = 0.3, ω = 0.525, k = 4 × 10⁷, l = 2.1 × 10⁷, α = 1, π = 0.1, μ₋ = μ₊ = 0.1, φ = 0.67, δ ∼ 10⁻⁴, a = 7.

Fig. 4.

Epidemic curves, epidemics induced by phage instability. Initial phage density was set to zero; phage are provided by a small input from phage-infected individuals. y axis, number of disease cases; x axis, time in weeks; φ (ω, a), solid line, 1.5 (0.525, 7); dashed line, 2.0 (0.394, 7); dotted line, 3.0 (0.263, 5); dot-dashed line, 5.0 (0.158, 3). (Inset) Bacteria and phage densities over time, φ = 1.5, δ ∼ 5 × 10⁻⁵. Other parameters as in Fig. 3.

Fig. 5.

Increase in phage-infected cholera patients. y axis, proportion of infected individuals harboring phage; x axis, time in weeks. Phage median infectious dose (l): solid line, 10⁶; dotted line, 10⁵; dot-dashed line, 10⁴. (A) Bloom-induced epidemic, initial bacterial density 3 × K_v, initial phage density 7.2 × 10⁵ virions per liter, φ = 0.67. (B) Instability-induced epidemic, initial phage density 7.2 × 10⁵ = 0.01 × equilibrium density, zero initial phage-positive individuals, φ = 1.5. Other parameters as in Fig. 3.