Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir

Abstract

. The objective is to explore the role of the aquatic reservoir on the persistence of endemic cholera as well as to define minimum conditions for the development of epidemic and endemic cholera. The reproduction rate of cholera in a community is defined by the product of social and environmental factors. The importance of the aquatic reservoir depends on the sanitary conditions of the community. Seasonal variations of contact rates force a cyclical pattern of cholera outbreaks, as observed in some cholera-endemic communities. infection in endemic populations as well as a better description of the relationship between dose and virulence.

Background

. The objective is to explore the role of the aquatic reservoir on the persistence of endemic cholera as well as to define minimum conditions for the development of epidemic and endemic cholera.

Results

The reproduction rate of cholera in a community is defined by the product of social and environmental factors. The importance of the aquatic reservoir depends on the sanitary conditions of the community. Seasonal variations of contact rates force a cyclical pattern of cholera outbreaks, as observed in some cholera-endemic communities.

Conclusions

infection in endemic populations as well as a better description of the relationship between dose and virulence.

Background

O139), which colonizes the small intestine and produces an enterotoxin responsible for a watery diarrhea. Without prompt treatment, a person with cholera may die of dehydration in a matter of hours after infection. Cholera outbreaks are generally associated to contaminated food and water supplies. Appropriate sanitation and safe water are the main weapons against this disease.

] and Latin America in 1991. The occurrence of successive cholera outbreaks throughout Africa and Latin America during the 90's raised the concern that cholera had established itself in these regions as an endemic disease.

]. How important they are and how they interact with each other and with other variables to drive cholera epidemiology, are open questions.

in endemic regions. What is the role of the aquatic reservoir in promoting epidemic and endemic cholera? What regions are more likely to maintain endemic cholera? What are the best approaches to prevent and control cholera outbreaks? What are the best predictors of the fate of a community after the introduction of cholera?

]. They can synthesize the current empirical knowledge about the disease into a coherent mechanistic framework. These models may help us to infer causal relationships and to suggest experimental designs to test alternative hypotheses.

This work is structured in three parts. First, the mathematical model for epidemic and endemic cholera is presented. Secondly, the proposed model is applied to three hypothetical communities to simulate cholera-free, epidemic and endemic situations. Thirdly, I consider possible causes of endemic oscillations. I finish this work discussing insights brought from model analyses into cholera dynamics.

Mathematical Model

]. The mathematical model is:

)

) may also grow in the water at a rate determined by environmental factors (temperature, for example).

Dose-dependent infection rate.

Symbols used in the model

in water that yields 50% chance of catching cholera. I assume that the only route for infection is the ingestion of contaminated water from non-treated sources.

]. It is not clear, however, if inoculum size is directly related to virulence or if it just increases the chance of intestine colonization. Here, I assumed that inoculum size affects the per capita infection rate (i.e., the probability of colonization), but not the severity of symptoms. Equation 1b states that the infected population increases as susceptibles become infected (first term in the equation) and decreases as they recover from the disease or die.

.

At last, equations (2) specify the initial conditions (all individuals are initially susceptible).

First case: cholera-free population

Consider a community that does not experience cholera for generations. All individuals are susceptibles. There are neither infective or immune individuals nor toxigenic bacteria in the water.

). This threshold is given by:

= 1); the introduction of infectives will trigger an outbreak.

in the water. It decreases, on the other hand, as contamination of water supplies as well as contact with these waters increase. In other words, the better water quality and sewage treatment are, the greater must be the pool of susceptibles in order to trigger a cholera outbreak.

Rearranging equation 5, we find the maximum degree of contamination each infected person may cause to the water reservoir without causing public health hazards:

as

/7 = ca. 5700 liters of water per infected person per day.

is found associated to phytoplankton, macrophyte, zooplankton, crustacea and other aquatic organisms. On the surface of these organisms, density of bacteria may be 100 to 1000 times greater than in the aquatic medium. These organisms are not evenly distributed within the water body. Phytoplankton tends to concentrate on the water surface, zooplankton migrates along the water column on a daily basis. If water is taken from phyto- or zooplankton-rich patches, risk of catching cholera will increase, enhancing the probability of triggering an outbreak in the community.

This model is too simple to provide quantitative predictions on cholera dynamics. Nevertheless, its qualitative results verifies known alternative approaches to the prevention of cholera outbreaks:

. The smaller these parameters are, the larger must be the susceptible pool in order to a cholera outbreak to develop (equation 5).

2. Dilute cholera diarrhea with large amounts of water to make water uninfective.

Second case: Epidemic cholera

):

). The simulation starts with 10,000 susceptibles. The arrival of an infected individual triggers an outbreak. Bacterial density in the water (dashed black line) increases as result of human excretion. The epidemic curve (red solid line) starts to decline when the number of susceptibles crosses down the threshold line Sc.

population eventually goes extinct. Community 2, then, returns to the cholera-free steady state.

), cholera prevalence oscillates until it reaches a steady-state. Oscillations are triggered when the number of susceptibles exceed the Sc threshold (dashed line).

Third case: Endemic cholera

). Setting the derivatives of equation system 1 to zero and solving it algebraically, we obtain the endemic equilibrium:

), where φ is

. This fraction is a function of human parameters, only.

].

, triggering a new outbreak. Eventually, the number of infectives stabilizes into a fixed fraction of the population. Bacterial dynamics in the water is also oscillatory and follows the human excretion pattern.

), the threshold tend to zero, and community of any size in contact with the reservoir should be subject to an outbreak.

)

in equation 1 by the sin function:

).

Parameter values used in the sensitivity analysis.

), the shorter is the period without any infection.

Simulation of a community that experiences seasonal contact with contaminated waters (due to periodic flooding, for example). Periodic fluctuation of the contact rate causes oscillations in the number of infections. During the low contact period, no infections occur. As contact increases (due to rising waters in a flooding area, for example), the probability of catching cholera increases. Outbreaks tend to occur sooner in larger populations. Dot-dashed line shows the number of infections in a population with 1,000 individuals, dashed line in a 5,500 population and dotted line in a 100,000 population. In large populations, the seasonal outbreak may be followed by a period with relatively constant incidence as contact rate continues high.

)

in equation system 1 was replaced by the periodic function:

).

. Seasonal decay of water quality triggers periodic outbreaks that are followed by a period of approximately constant prevalence.

A prevalence "plateau" often follows the annual cholera outbreak. The dynamics is very similar to that observed for the scenario 1. For some parameter combinations, however, this plateau rises to form a second outbreak of minor intensity. Conditions favoring the occurrence of this second peak include high K, high extinction rate and fast recover rate.

)

in equation system 1 was replaced by the periodic function:

in the environment has been linked to factors as temperature, copepod abundance and chlorophyll. However, the mechanistic relationships between these variables are still not clearly defined and I opted for not including them explicitly in the model.

).

in the environment also triggers seasonal outbreaks of cholera.

Discussion

.

].

in the water in the simplest way possible, i.e., with density independent growth and death rates. This model is quite abstract but provides some insights about the role of an environmental reservoir on cholera epidemiology.

infection is dose-dependent. It is likely a minimal reservoir should be required for the occurrence of cholera cases in the population.

), the shorter can be the bacterial residence time in the water. In the limit, we may say that endemism in sanitized communities requires a permanent reservoir while endemism in poor communities requires just transient reservoirs (and a sufficiently high turnover of susceptibles).

].

).

Periodicity of reported cases of cholera in the Brazilian Central Amazon region. This region is characterized by seasonal flooding of the Negro and Amazon Rivers, driven mainly by snow melt in the Andean headwaters of the Amazon River.

Conclusion

environmental reservoir. The model proposed is very simple and does not include many features of this complex system. Nonetheless, this study brings some new insights into cholera epidemiology. Most studies on cholera epidemiology concentrate on either social or environmental factors. This work, however, shows that the reproduction rate of cholera is a function of social and environmental factors. It is necessary to determine the relative weights of each one of these components in order to develop appropriate control strategies.

infection in endemic populations. We also need better estimates of the required infection dose as well as a better description of the relationship between dose and virulence.

Pre-publication history

The pre-publication history for this paper can be accessed here:

Appendix

Stability analysis.

Click here for additional data file

Acknowledgments

I would like to thank Dr. Bradley Sack and Dr. Russek-Cohen for providing critiques of this manuscript. Support was provided by FAPERJ, FINEP and PRONEX.