Stability, bifurcation and chaos analysis of vector-borne disease model with application to Rift Valley fever

摘要: This paper investigates a RVF epidemic model by qualitative analysis and numerical simulations. Qualitative have been used to explore the stability dynamics of equilibrium points while visualization techniques such as bifurcation diagrams, Poincare maps, maxima return maps largest Lyapunov exponents are numerically computed confirm further complexity these induced seasonal forcing on mosquitoes oviposition rates. The obtained results show that ordinary differential equation models with external can rich dynamic behaviour, ranging from strange attractors which may explain observed fluctuations found in empiric outbreak data, well non deterministic nature inter-epidemic activities. Furthermore, coexistence endemic is subjected existence certain number infected Aedes mosquitoes, suggesting potential initiate epidemics through transovarial transmission sustain low levels disease during post periods. Therefore we argue locations serve virus reservoirs should be eliminated or kept under control prevent multi-periodic outbreaks consequent chains infections. epidemiological significance this study is: (1) birth rate (in both Culex) trigger unpredictable outbreaks; (2) more likely capable inducing behaviour compared Culex; (3) higher rates do not general imply manifestation irregular disease. Finally, our vector able mimic linear increase livestock seroprevalence period showing constant exposure presence active foci. suggests partly build upon Therefore, surveillance recommended.