Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks
Spatial pattern formation in activator-inhibitor models with nonlocal dispersal
On some reaction-diffusion equations generated by non-domiciliated triatominae, vectors of Chagas disease
Nabahats Dib-Baghdadli 1,, , Rabah Labbas 2, , Tewfik Mahdjoub 1, and Ahmed Medeghri 3,
NLAAML, Abou-Bekr Belkaid University, Tlemcen 13000, Algeria
Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, 76600 Le Havre, France
LMPA, Abdelhamid Ibn-Badis University, Mostaganem 27000, Algeria
* Corresponding author: Nabahats Dib-Baghdadli
Figure(2) / Table(1)
In this work, we study some reaction-diffusion equations set in two habitats which model the spatial dispersal of the triatomines, vectors of Chagas disease. We prove in particular that the dispersal operator generates an analytic semigroup in an adequate space and we prove the local existence of the solution for the corresponding Cauchy problem.
Keywords: Chagas disease, dispersal process, reaction-diffusion equations, skew brownian motion, sectorial operator.
Mathematics Subject Classification: Primary:35K57, 47D06;Secondary:92B05, 12H20.
Citation: Nabahats Dib-Baghdadli, Rabah Labbas, Tewfik Mahdjoub, Ahmed Medeghri. On some reaction-diffusion equations generated by non-domiciliated triatominae, vectors of Chagas disease. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021004
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Figure 1. Population density in two habitats
Figure 2. A schematic representation of the life cycle used in the triatomine's model
Table 1. The demographic and diffusion parameters of T.Dimidiata population
Parameter Definition Properties
$ s_{j}(t) $ Probability of survival of juveniles per unit of time $ 0\leq s_{j}(t)\leq 1 $
$ s_{a}(t) $ Probability of survival of adult per unit of time $ 0\leq s_{a}(t)\leq 1 $
$ w_{j}(t) $ Probability of transition from juvenile to adult $ 0\leq w_{j}(t)\leq 1 $
$ f_{a}(t) $ Female fertility per unit time $ f_{a}(t)\geq 0 $
$ d_{j-},d_{j+} $ diffusion coefficient of juveniles $ d_{j-},d_{j+}> 0 $
$ d_{a-},d_{a+} $ diffusion coefficient of adults $ d_{a-},d_{a+}> 0 $
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Nabahats Dib-Baghdadli Rabah Labbas Tewfik Mahdjoub Ahmed Medeghri