Host resistance, population structure and the long-term persistence of bubonic plague: contributions of a modelling approach in the Malagasy focus

Abstract

Although bubonic plague is an endemic zoonosis in many countries around the world, the factors responsible for the persistence of this highly virulent disease remain poorly known. Classically, the endemic persistence of plague is suspected to be due to the coexistence of plague resistant and plague susceptible rodents in natural foci, and/or to a metapopulation structure of reservoirs. Here, we test separately the effect of each of these factors on the long-term persistence of plague. We analyse the dynamics and equilibria of a model of plague propagation, consistent with plague ecology in Madagascar, a major focus where this disease is endemic since the 1920s in central highlands. By combining deterministic and stochastic analyses of this model, and including sensitivity analyses, we show that (i) endemicity is favoured by intermediate host population sizes, (ii) in large host populations, the presence of resistant rats is sufficient to explain long-term persistence of plague, and (iii) the metapopulation structure of susceptible host populations alone can also account for plague endemicity, thanks to both subdivision and the subsequent reduction in the size of subpopulations, and extinction-recolonization dynamics of the disease. In the light of these results, we suggest scenarios to explain the localized presence of plague in Madagascar.

Figure 1. Equilibrium states for a susceptible population, according to the rats' maximal birth rate, , and the transmission rate, , with (a) rats and (b) rats.

Values for other parameters follow the ones presented in Table 1. Stable equilibrium states: (,) in black, (,) in dark grey and (,) in light grey. The dynamics for four couples of parameters are given on Supporting Figure S4.

Figure 2. Equilibrium states for a rat population including resistant rats, according to the maximal birth rate of rats,, and the transmission rate, .

Parameter values are given in Table 1, rats. Stable equilibrium states: (,,) in black, (,,) in dark grey, (,,) in light grey and (,,) in white. The dynamics for four couples of parameters are given on Supporting Figure S8.

Figure 3. Equilibrium states for a susceptible host metapopulation composed of (a) 2 subpopulations, (b) 4 subpopulations and (c) 25 subpopulations (deterministic analysis).

Total carrying capacity =  rats. Other parameter values are given in Table 1. Stable equilibrium states: (,) in black, (,) in dark grey and (,) in light grey.

Figure 4. Estimated probability of persistence of susceptible rats and infectious rats through time, in (a) one non structured population of rats, (b) 4 subpopulations with total rats (ie, rats per subpopulation), and (c) one non structured population of rats.

This probability was estimated on 100 simulations. , and other parameter values are given in Table 1. The Supporting Figure S10 illustrates, for one of the simulations in (b), the extinction-recolonization dynamics of the disease which occur between the subpopulations.