Modeling Optimal Intervention Strategies for Cholera

Abstract

While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate a mathematical model to include essential components such as a hyperinfectious, short-lived bacterial state, a separate class for mild human infections, and waning disease immunity. A new result quantifies contributions to the basic reproductive number from multiple infectious classes. Using optimal control theory, parameter sensitivity analysis, and numerical simulations, a cost-effective balance of multiple intervention methods is compared for two endemic populations. Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods.

An age-structured model for the spread of epidemic cholera: Analysis and simulation

“…The results obtained by varying the rate of shedding motivate ideas on the different treatment options that may be possible with this age-structured model and its implementation. Combination treatments in an ordinary differential equation setting have been introduced and theoretically analyzed in [30]. The inclusion of treatment control strategies in an age-structured cholera model will be presented in future work.…”

“…A common type of model for the spread of an infectious disease is an SIR model, so named after the categorization of individuals in the classes of susceptible, infected, and recovered populations [8]. SIR models of cholera developed so far are time-dependent models which give rise to a system of ordinary differential equations (ODEs); see [10,11,22,24,30].…”

“…The work by Miller Neilan et al [30] investigated optimal control of three strategies to slow the spread of the disease in ODE model with hyperinfectious vibrios, asymptomatic infecteds and waning immunity. There is another modeling approach with a compartment that tracks pathogen in the water; this approach gives a SIWR system of four ODEs and was used to simulate cholera in the 19th century in London, [40,41].…”

Examination of models for cholera: insights into model comparison methods

“…Possibly due to the limited data available to modellers, it is difficult to justify the mathematical use of a complex mechanistically-driven model, because accurate and unique parameterizations for these models cannot be obtained. The modelling literature contains a spectrum of deterministic models from very simple to more complex structures (Andrews & Basu, 2011;Eisenberg, Robertson, & Tien, 2013;Hartley, Morris, Jr., & Smith, 2005;King, Ionides, Pascual, & Bouma, 2008;Mukandavire et al, 2011;Miller Neilan,Schaefer, Gaff, Fister, & Lenhart, 2010;Rinaldo et al, 2012;Tuite et al, 2011). We note that some researchers complement a relatively simple deterministic model with complex spatial considerations and migration.…”

An evolutionary computing approach for parameter estimation investigation of a model for cholera

“…The ultimate goal, of course, of these efforts is to better understand the dynamics of a cholera outbreak so that we can greatly reduce the morbidity which results from the disease. There is a disconnect between the mechanistic understanding that we can infer from a microbiology/human studies perspective [2,5,11,21,26,27,[30][31][32][33][34]36,40] and the simplified models chosen, in part, due to the limited data available to justify parameter choices for more complex models [7,28,29,37,41,42]. Compounding this disparity is the inconsistency regarding choices for key parameter values across many carefully researched papers by top scientists.…”