Global Stability of Equilibria for a Metapopulation S-I-S Model

摘要: Standard models for the dynamics of infection disease are based on as-sumption homogeneous mixing among individuals. However, individualsare generally aggregated in patches (pieces woodland, farms, households,villages...) and transmission is much easier within thanfrom one patch to other.Different approaches have been used handle “patchy” structure ofpopulations, that run from individual-based simulation (see, in-stance, [11] avian flu Thailand) systems differential equations forthe classes at each instance, [2]). An interesting ap-proach use “spatially implicit metapopulation models”: these, thediscretenatureofindividualandpatchesisclearlyretained,sothateachpatchhas always an integer number infectives; however, spatial arrangementof not considered, so same anyother patch.Following a long tradition stochastic transmissionwithin between households[5], Ball [4] has derived deterministic systemfor epidemic SIS type spreading population distributed infinitenumber households, size N; outside households isassumed be random. The system can obtained [9] as limit, Mgoes infinity, corresponding model with finite Mof households. This system, which focus this contribution, will bepresented detail next Section. obtains complete results onthe stability endemic equilibrium N = 2 numerical simulationsare given ≥ 3. Arrigoni Pugliese [3] compute reproduction ratioR