| Abstract: |
| Vector-borne diseases are contagious diseases and it is spreaded by vectors. Vectors are living organisms can spread contagious diseases between from one host (carrier) to another. In this work, we discuss the problem of the nonlinear coupled reaction-diffusion equation, which incorporates the vector-borne diseases with vertical transmission and cure. The total population size can be divided into human hosts and vectors are denoted by $N_1$ and $N_2$. The host population can be divided into four subclasses represented by $S$, $I$, $T$, and $R$ for the susceptible, infectious, under treatment and recovered classes. Thus, $N_1=S+I+T+R$. The main aim of this work is to investigate the existence and uniqueness of weak solution of the above proposed model. Finally, numerical examples are given to illustrate the validity of theoretical results. |
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