Persistence of mosquito vector and dengue: Impact of seasonal and diurnal temperature variations

Figure 2.1.  A schematic diagram of the dengue transmission model. $ A, M_s, M_e, M_i $: aquatic, susceptible, exposed, and infected mosquitos. $ H_s, H_e, H_i, H_r $: susceptible, exposed, infected, and recovered humans. Solid arrows represent birth, maturation, infection, transfer, death, while dashed arrows indicate the effects of time dependent periodic environmental temperature, $ T(t) $

Figure 2.2.  Best-fit curves provided by the experimental data [44] for $ \delta (T) $ (oviposition rate), $ \mu_a(T) $ (aquatic phase mortality rate), $ \theta (T) $ (mosquito emergence rate from acuatic phase), and $ \mu_m(T) $ (mosquito mortality rate)

Figure 2.3.  Best-fit curve provided by the data generated from the previous estimates [17] for the transmission probability from human to mosquito, $ \beta_m (T) $

Figure 2.4.  Temperature profile of $ T_m(t) $ [Left], $ \Psi_d(t) $ [Middle], and $ T(t) $ [Right]. Parameters used are $ T_0 = 25 ^oC, \epsilon_m = 5 ^oC, \tau_m $ = 365 day, $ \phi_m = 0 $, $ \epsilon_d = 5 ^oC $, $ \tau_d = 1 $ day, and $ \phi_d = 0 $

Figure 4.1.  Mosquito reproduction number ($ \mathcal{R}^M $) [Left] and infection invasion threshold ($ \mathcal{R}^0 $) [right] for different values of the mean temperature ($ T_0 $) with amplitudes of seasonal temperature and diurnal temperature fixed at $ \epsilon_m = 5 $ $ ^oC $ and $ \epsilon_d = 5 $ $ ^oC $, respectively. For comparison purposes, $ \mathcal{R}^M $ and $ \mathcal{R}^0 $ for the constant temperature (i.e., $ \epsilon_m = \epsilon_d = 0 $ $ ^oC $) are also plotted

Figure 4.2.  Mosquito reproduction number ($ \mathcal{R}^M $) [left column] and infection invasion threshold ($ \mathcal{R}^0 $) [right column] for different values of the amplitudes of seasonal temperature ($ \epsilon_m $) with the amplitude of diurnal temperature fixed at $ \epsilon_d = 5 $ $ ^oC $ and the mean temperature fixed at $ T_0 = 16 $ $ ^oC $ [top row], $ T_0 = 28 $ $ ^oC $ [middle row], and $ T_0 = 38 $ $ ^oC $ [bottom row]

Figure 4.3.  Mosquito reproduction number ($ \mathcal{R}^M $) [left column] and infection invasion threshold ($ \mathcal{R}^0 $) [right column] for different values of the amplitudes of diurnal temperature ($ \epsilon_d $) with the amplitude of seasonal temperature fixed at $ \epsilon_m = 5 $ $ ^oC $ and the mean temperature fixed at $ T_0 = 16 $ $ ^oC $ [top row], $ T_0 = 28 $ $ ^oC $ [middle row], and $ T_0 = 38 $ $ ^oC $ [bottom row]