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In this paper, we study a more general diffusive spatially dependent vaccination model for infectious disease. In our diffusive vaccination model, we consider both therapeutic impact and nonlinear incidence rate. Also, in this model, the number of compartments of susceptible, vaccinated and infectious individuals are considered to be functions of both time and location, where the set of locations (equivalently, spatial habitats) is a subset of $ \mathbb {R}^n $ with a smooth boundary. Both local and global stability of the model are studied. Our study shows that if the threshold level $ \mathcal {R}_0 \le 1, $ the disease-free equilibrium $ E_0 $ is globally asymptotically stable. On the other hand, if $ \mathcal {R}_0> 1 $ then there exists a unique stable disease equilibrium $ E^* $ . The existence of solutions of the model and uniform persistence results are studied. Finally, using finite difference scheme, we present a number of numerical examples to verify our analytical results. Our results indicate that the global dynamics of the model are completely determined by the threshold value $ \mathcal {R}_0 $ .

Background: Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, and social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 obligation among the Rohingya refugees of Bangladesh to keep up with the disease outbreak’s pace, health needs, and disaster preparedness. Methodology and Findings: To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a modified Susceptible-Exposed-Infectious-Recovered (SEIR) transmission model. All of the values of different parameters used in this model were from the Bangladesh Government’s database and the relevant emerging literature. We addressed two different scenarios, i.e., the best-fitting model and the good-fitting model with unique consequences of COVID-19. Our best fitting model suggests that there will be reasonable control over the transmission of the COVID-19 disease. At the end of December 2020, there will be only 169 confirmed COVID-19 cases in the Rohingya refugee camps. The average basic reproduction number (R0) has been estimated to be 0.7563. Conclusions: Our analysis suggests that, due to the extensive precautions from the Bangladesh government and other humanitarian organizations, the coronavirus disease will be under control if the maintenance continues like this. However, detailed and pragmatic preparedness should be adopted for the worst scenario.

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

Background: Besides maintaining health precautions, vaccination has been the only prevention from SARS-CoV-2, though no clinically proved 100% effective vaccine has been developed till date. At this stage, to withhold the debris of this pandemic-experts need to know the impact of the vaccine efficacy rates, the threshold level of vaccine effectiveness and how long this pandemic may extent with vaccines that have different efficacy rates. In this article, a mathematical model study has been done on the importance of vaccination and vaccine efficiency rate during an ongoing pandemic. Methods: We simulated a five compartment mathematical model to analyze the pandemic scenario in both California, and whole U.S. We considered four vaccines, Pfizer (95%), Moderna (94%), AstraZeneca (79%), and Johnson & Johnson (72%), which are being used rigorously to control the SARS-CoV-2 pandemic, in addition with two special cases: a vaccine with 100% efficacy rate and no vaccine under use. SARS-CoV-2 related data of California, and U.S. were used in this study. Findings: Both the infection and death rates are very high in California. Our model suggests that the pandemic situation in California will be under control in the last quartile of the year 2023 if vaccination program is continued with the Pfizer vaccine. During this time, six waves may happen from the beginning of the immunization where the case fatality and recovery rates will be 1.697% and 98.30%, respectively. However, according to the considered model, this period might be extended to the mid of 2024 when vaccines with lower efficacy rates are used. On the other hand, the daily cases and deaths in the U.S. will be under control at the end of 2026 with multiple waves. Although the number of susceptible people will fall down to none in the beginning of 2027, there is less chance to stop the vaccination program if vaccinated with a vaccine other than a 100% effective vaccine or Pfizer, and at that case vaccination program must run till the mid of 2028. According to this study, the unconfirmed-infectious and infected cases will be under control at the end of 2027 and at the mid of 2028, respectively. Interpretation: The more effective a vaccine is, the less people suffer from this malign infection. Vaccines which are less than 90% effective do not have notable contribution to control the pandemic besides hard immunity. Furthermore, specific groups of people are getting prioritized initially, mass vaccination and quick responses are required to control the spread of this disease.