In this study, we propose a new mathematical model and analyze it to understand the transmission dynamics of the COVID-19 pandemic in Bangkok, Thailand. It is divided into seven compartmental classes, namely, susceptible S , exposed E , symptomatically infected I s , asymptomatically infected I a , quarantined Q , recovered R , and death D , respectively. The next-generation matrix approach was used to compute the basic reproduction number denoted as R cvd 19 of the proposed model. The results show that the disease-free equilibrium is globally asymptotically stable if R cvd 19 < 1 . On the other hand, the global asymptotic stability of the endemic equilibrium occurs if R cvd 19 > 1 . The mathematical analysis of the model is supported using numerical simulations. Moreover, the model’s analysis and numerical results prove that the consistent use of face masks would go on a long way in reducing the COVID-19 pandemic.

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In this paper, we prove some coincidence and fixed point theorems for a new type of multi-valued weak G-contraction mapping with compact values. The results of this paper extend and generalize several known results from a complete metric space endowed with a graph. Some examples are given to illustrate the usability of our results. MSC: 47H04; 47H10

A dynamical model for COVID-19 spread relating to non-pharmaceutical interventions and vaccination is mathematically generated by adding a gradual vaccination compartment for the susceptible population and considering only a symptomatic infectious stage. In our model, there are seven compartments dividing a given population into susceptible (S), vaccinated (V ), exposed (E), infected (I), quarantined (Q), recovered (R) and death (D) groups, respectively. Then, theoretically analysis is given by investigating the COVID-19 free and endemic equilibrium points, and computing the vaccination reproduction number of this model denoted as R vac using the next generation matrix. If R vac > 1, then the COVID-19 transmission increases exponentially and depends on vaccine efficacy. On the other hand, if R vac < 1, then there occurs the COVID-19 disease eradication. The risk from infection can be importantly reduced whenever the intake of COVID-19 vaccines exceeds one dose. The numerical results reveal that the nonpharmaceutical ways and the administered COVID-19 vaccines can be effective against the current variants of COVID-19, and the additional efforts such as a third vaccine booster shot should be considered and implemented to greatly mitigate the risks of emerging variants of the COVID-19 virus. Moreover, combining different types of COVID-19 vaccines can be appeared as a possible way to give better protection against COVID-19 as well.

In this paper, we define a new class of Reich type multi-valued contractions on a complete metric space satisfying the g-graph preserving condition and we study the fixed point theorem for such mappings. In addition, we present the existence and uniqueness of the fixed point for at least one of two multi-valued mappings. The results of this paper extend and generalize several well-known results. Some examples illustrate the usability of our results. MSC: 47H04; 47H10