Estimating the reproductive numbers for the 2008–2009 cholera outbreaks in Zimbabwe

Abstract

Cholera remains an important global cause of morbidity and mortality, capable of causing periodic epidemic disease. Beginning in August 2008, a major cholera epidemic occurred in Zimbabwe, with 98,585 reported cases and 4,287 deaths. The dynamics of such outbreaks, particularly in nonestuarine regions, are not well understood. We explored the utility of mathematical models in understanding transmission dynamics of cholera and in assessing the magnitude of interventions necessary to control epidemic disease. Weekly data on reported cholera cases were obtained from the Zimbabwe Ministry of Health and Child Welfare (MoHCW) for the period from November 13, 2008 to July 31, 2009. A mathematical model was formulated and fitted to cumulative cholera cases to estimate the basic reproductive numbers R 0 and the partial reproductive numbers from all 10 provinces for the 2008–2009 Zimbabwe cholera epidemic. Estimated basic reproductive numbers were highly heterogeneous, ranging from a low value of just above unity to 2.72. Partial reproductive numbers were also highly heterogeneous, suggesting that the transmission routes varied by province; human-to-human transmission accounted for 41–95% of all transmission. Our models suggest that the underlying patterns of cholera transmission varied widely from province to province, with a corresponding variation in the amenability of outbreaks in different provinces to control measures such as immunization. These data underscore the heterogeneity of cholera transmission dynamics, potentially linked to differences in environment, socio-economic conditions, and cultural practices. The lack of traditional estuarine reservoirs combined with these estimates of R 0 suggest that mass vaccination against cholera deployed strategically in Zimbabwe and surrounding regions could prevent future cholera epidemics and eventually eliminate cholera from the region.

Disease dynamics in a coupled cholera model linking within-host and between-host interactions

“…Write K = (k ij ). Particularly, if n = 2, the type reproduction T can be easily defined in terms of the elements k ij T 1 = k 11 + k 12 k 21 1 − k 22 ,…”

“…Here we consider a model system that couples the between-host and withinhost dynamics and the interaction between humans and the environment. We use a susceptible-infected-recovered-susceptible epidemic framework [21,34] to describe the between-host dynamics:…”

“…We do impose slightly stronger conditions on β H (h(B)) than that for ξ(h(B)), partly due to the fact that the direct transmission rate is typically very sensitive to system dynamics in a cholera model [21].…”

“…However, to the best of our knowledge, no existing work has attempted to address the coupled within-and between-host dynamics of cholera (a severe water-borne gastroenteric disease caused by the bacterium Vibrio cholerae), despite the fact that a large body of work has been devoted to its population level modelling (e.g. [4][5][6]17,21,22,26,28,29,[32][33][34][35][36]). It is also worth mentioning that some of these between-host models have incorporated both human and environmental transmission pathways with nonlinear disease incidence functions (see, e.g.…”

A Study of a Fractional-Order Cholera Model

“…This model emphasizes the stage of explosive infectivity of V. cholerae, based on the laboratory measurements that freshly shed V. cholerae from human intestines outcompeted other V. cholerae by as much as 700-fold for the first few hours in the environment [1,5]. Recently, Mukandavire et al [14] proposed a model to estimate the reproduction number for the 2008-2009 cholera outbreak in Zimbabwe. Their model includes both environment-to-human and human-to-human transmission pathways.…”