Mathematical assessment of the role of environmental factors on the dynamical transmission of cholera

Abstract

a b s t r a c tIn this paper, we investigate the impact of environmental factors on the dynamical transmission of cholera within a human community. We propose a mathematical model for the dynamical transmission of cholera that incorporates the virulence of bacteria and the commensalism relationship between bacteria and the aquatic reservoirs on the persistence of the disease. We provide a theoretical study of the model. We derive the basic reproduction number R 0 which determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever R 0 ≤ 1 , while when R 0 > 1 , the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is locally asymptotically stable on a positively invariant region of the positive orthant. The sensitivity analysis of the model has been performed in order to determine the impact of related parameters on outbreak severity. Theoretical results are supported by numerical simulations, which further suggest the necessity to implement sanitation campaigns of aquatic environments by using suitable products against the bacteria during the periods of growth of aquatic reservoirs.

Congruity of genomic and epidemiological data in modelling of local cholera outbreaks

“…Many cholera models in the literature include an environmental compartment [17][18][19][20][21]. Such an environmental compartment is typically introduced to explicitly model the transmission of infection through a water source, and additionally describes the evolution of bacteria in a water source with temperature-dependent dynamics.…”

“…Our modelling choices are aimed at simplicity and driven by the overall goal of checking the consistency between these data sources. For instance, we deliberately take an agnostic stance on the open questions related to the role of the environment or details of bacterial dynamics: while several previous studies explicitly included the environmental compartment [17][18][19][20][21] leading to a larger number of model parameters, we chose to model cholera dynamics as an effective transmission process which includes a periodic functional dependence on seasonality, similarly to the approach of Peak et al [22]. To account for discreteness in observed cases, we propose a novel sampling model which relates the continuous model with the discrete observed case counts.…”

Modeling the effects of information‐dependent vaccination behavior on meningitis transmission

“…Proof This result can be obtained by checking that all the (five) hypotheses of Theorem 4.3 in Kamgang and Sallet 39 are satisfied. This procedure is well known and used elsewhere (see, e.g., Theorem 2 in the recent paper 40 ). For our model, the result can be obtained in the same way.…”

Modeling the effects of information-dependent vaccination behavior on meningitis transmission

“…This result can be obtained by checking that all the (five) hypotheses of Theorem 4.3 in [23] are satisfied. This procedure is well known and used elsewhere (see for example, Theorem 2 in the recent paper [24]). For our model the result can be obtained in the same way.…”