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| Malaria is an infectious disease transmitted by mosquitoes, and this paper focuses on two different regions due to differences in prevention and control measures such as vaccination. When a movement of population and mosquitoes occurs between two patches, under what conditions will malaria eventually extinct or continue to spread. This article takes the basic regeneration number as the threshold parameter. When $\mathscr{R}_0< 1$ the disease will die out and when $\mathscr{R}_0> 1$ the disease will persist. In section 5, through numerical simulation, we found that rational distribution of vaccine number between two patches can minimize $\mathscr{R}_0$ and minimize the total number of infections when the number of vaccine is limited. The results show that the distribution of vaccine number is different from the conventional idea that the distribution is based on the patches population ratio. Due to the influence of population movement between patches, the optimal strategy for vaccine distribution needs to be based on the actual situation. |
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| Keywords:Applied Mathematics, Malaria model, Vaccinations, Patches structure, Optimal strategy. |
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