Abstract
Mosquitoes play an important role in the spread of mosquito-borne diseases. Considering the sensitivity of mosquitoes’ aquatic stage to the seasonal shift, in this paper, we present a seasonally forced mosquito-borne epidemic model by incorporating mosquitoes’ aquatic stage (eggs, larvae, and pupae) and seasonal shift factor, which is a periodic discontinuous differential system. Firstly, some sufficient conditions for the existence and uniqueness of a disease-free solution are obtained. Further, we define the basic reproduction number mathcal{R}_{0}, and obtain the stability of the disease-free solution when mathcal{R}_{0} is less than one. And, if mathcal{R}_{0} is greater than one, the mosquito-borne disease is uniformly persistent and the model admits a positive periodic solution. Finally, some numerical simulations are given to illustrate the main theoretical results. In addition, simulation results also imply that ignoring the effects of seasonal succession can overestimate or underestimate mosquito-borne disease trends.
Highlights
In recent years, the spread of mosquito-borne diseases has been characterized by high morbidity, high mortality, rapid growth in the number of cases, etc., which has become the major public health concern in the tropical and sub-tropical regions of the world
Based on the above discussion, in this paper, we propose a mosquito-borne disease transmission model with seasonal variation, which is a periodic discontinuous differential system
We obtain the basic reproduction number R0 ≈ 2.2784, which is close to the basic reproduction number R0 ≈ 2.2678 > 1 in Fig. 2, where the seasonal succession is considered
Summary
The spread of mosquito-borne diseases (such as dengue fever, malaria, Zika, chikungunya, yellow fever, and so on) has been characterized by high morbidity, high mortality, rapid growth in the number of cases, etc., which has become the major public health concern in the tropical and sub-tropical regions of the world. Based on the above discussion, in this paper, we propose a mosquito-borne disease transmission model with seasonal variation, which is a periodic discontinuous differential system. (H1) Considering the influence of seasonal factors (such as humidity, temperature, etc.) on mosquitoes’ reproduction rate and breeding sites, we assume that the recruitment rate of the aquatic mosquitoes is governed by a logistic equation, in which these coefficients are periodic functions on account of seasonal effects. Lemma 2 If φ2b2 > (φ1 +μa1)μm, model (3) is persistent and has a positive ω-periodic solution (A∗(t), Sm∗ (t)). As consequence of Lemmas 1 and 2, we can obtain that if φ2b2 > μm1(φ1 + μa1) and lim inft→∞ Θ(t) > 0, model (1) has a unique solution (Sh∗(t), 0, 0, A∗(t), Sm∗ (t), 0), which implies that the disease is extinct
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