Dynamics of a periodic Chikungunya model with temperature and rainfall effects. (English) Zbl 1454.34112
Summary: In this paper, a periodic Chikungunya model with temperature and rainfall effects is proposed and studied, which incorporates time-dependent extrinsic incubation period, time-dependent maturation delay, asymptomatic and symptomatic infectious humans. Two threshold parameters for the extinction and persistence of mosquitos and the virus are derived, respectively: the mosquito reproduction number \(\mathcal{R}_m\) and the basic reproduction number \(\mathcal{R}_0\). Then the analytic results are verified by numerical simulation with the temperature and rainfall data of the state of Ceará, where the largest outbreak in Brazil’s history occurred in 2017. And the effects of rainfall, seasonality, and asymptomatic infection in humans on mosquito population and the Chikungunya transmission are explored. Our simulations show that if these factors are not taken into account, the number of mosquito population and people infected may be overestimated. Finally, the relationships between \(\mathcal{R}_m\) and \(\mathcal{R}_0\) and some parameters are established.
MSC:
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 92D30 | Epidemiology |
| 34K13 | Periodic solutions to functional-differential equations |
| 34K20 | Stability theory of functional-differential equations |
| 34K25 | Asymptotic theory of functional-differential equations |
Keywords:
Chikungunya disease; time-dependent delays; asymptomatic infection; basic reproduction number; uniform persistenceReferences:
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