Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source

Modelling and control of cholera on networks with a common water source

“…see Figure 1 in [24]). The hub vertex is labelled as n + 1, corresponding to the common water source, while each leaf vertex is labelled as j, with 1 ≤ j ≤ n, corresponding to patch j.…”

“…When mass action incidence functions f j , g j and linear shedding functions h j are chosen as given in Equation (3), system (1) includes the model (31) in [24] as a special case, and thus Theorems 4.1 and 4.2 establish, for the first time, the complete global disease dynamics of the model in [24]. Namely, if the basic reproduction number R 0 in Equation (7) with p j , q j , r j as given in Equation (4) is not above one, then the disease-free equilibrium is globally asymptotically stable and cholera dies out from all patches, whereas if R 0 is above one, then there is a unique endemic equilibrium that is globally asymptotically stable and cholera persists at an endemic level in all patches.…”

“…The multi-patch cholera model (1)- (2) includes as a special case the model (31) in [24] in which the incidence functions f j , g j take the form of mass action, and shedding functions h j are linear, namely,…”

“…Our model includes and extends the model in [24] where mass action incidence is assumed for both transmission pathways. The proposed model can be regarded as a coupled system on a star network where the hub vertex corresponds to the common water source and the leaf vertices correspond to the patches where host live.…”

“…Thus it is difficult to apply these model studies to address spatial differences in the force of infection and effective disease control/intervention strategies. A multi-patch model has recently been proposed in [24] to address specifically the effect of a common water source on the transmission of cholera in a heterogeneous host population. Rigorous analysis has been carried out in [24] to show how heterogeneity affects the cholera invasibility in terms of the basic reproduction number R 0 and the efficacy of intervention measures.…”