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      The stability analysis of a co-circulation model for COVID-19, dengue, and zika with nonlinear incidence rates and vaccination strategies

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          Abstract

          This paper aims to study the impacts of COVID-19 and dengue vaccinations on the dynamics of zika transmission by developing a vaccination model with the incorporation of saturated incidence rates. Analyses are performed to assess the qualitative behavior of the model. Carrying out bifurcation analysis of the model, it was concluded that co-infection, super-infection and also re-infection with same or different disease could trigger backward bifurcation. Employing well-formulated Lyapunov functions, the model’s equilibria are shown to be globally stable for a certain scenario. Moreover, global sensitivity analyses are performed out to assess the impact of dominant parameters that drive each disease’s dynamics and its co-infection. Model fitting is performed on the actual data for the state of Amazonas in Brazil. The fittings reveal that our model behaves very well with the data. The significance of saturated incidence rates on the dynamics of three diseases is also highlighted. Based on the numerical investigation of the model, it was observed that increased vaccination efforts against COVID-19 and dengue could positively impact zika dynamics and the co-spread of triple infections.

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          Most cited references58

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          The global distribution and burden of dengue

          Dengue is a systemic viral infection transmitted between humans by Aedes mosquitoes 1 . For some patients dengue is a life-threatening illness 2 . There are currently no licensed vaccines or specific therapeutics, and substantial vector control efforts have not stopped its rapid emergence and global spread 3 . The contemporary worldwide distribution of the risk of dengue virus infection 4 and its public health burden are poorly known 2,5 . Here we undertake an exhaustive assembly of known records of dengue occurrence worldwide, and use a formal modelling framework to map the global distribution of dengue risk. We then pair the resulting risk map with detailed longitudinal information from dengue cohort studies and population surfaces to infer the public health burden of dengue in 2010. We predict dengue to be ubiquitous throughout the tropics, with local spatial variations in risk influenced strongly by rainfall, temperature and the degree of urbanisation. Using cartographic approaches, we estimate there to be 390 million (95 percent credible interval 284-528) dengue infections per year, of which 96 million (67-136) manifest apparently (any level of clinical or sub-clinical severity). This infection total is more than three times the dengue burden estimate of the World Health Organization 2 . Stratification of our estimates by country allows comparison with national dengue reporting, after taking into account the probability of an apparent infection being formally reported. The most notable differences are discussed. These new risk maps and infection estimates provide novel insights into the global, regional and national public health burden imposed by dengue. We anticipate that they will provide a starting point for a wider discussion about the global impact of this disease and will help guide improvements in disease control strategies using vaccine, drug and vector control methods and in their economic evaluation. [285]
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            Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.

            A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R0 1, then it is unstable. Thus, R0 is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R0 near one. This criterion, together with the definition of R0, is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control.
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              Zika virus outbreak on Yap Island, Federated States of Micronesia.

              In 2007, physicians on Yap Island reported an outbreak of illness characterized by rash, conjunctivitis, and arthralgia. Although serum from some patients had IgM antibody against dengue virus, the illness seemed clinically distinct from previously detected dengue. Subsequent testing with the use of consensus primers detected Zika virus RNA in the serum of the patients but no dengue virus or other arboviral RNA. No previous outbreaks and only 14 cases of Zika virus disease have been previously documented. We obtained serum samples from patients and interviewed patients for information on clinical signs and symptoms. Zika virus disease was confirmed by a finding of Zika virus RNA or a specific neutralizing antibody response to Zika virus in the serum. Patients with IgM antibody against Zika virus who had a potentially cross-reactive neutralizing-antibody response were classified as having probable Zika virus disease. We conducted a household survey to estimate the proportion of Yap residents with IgM antibody against Zika virus and to identify possible mosquito vectors of Zika virus. We identified 49 confirmed and 59 probable cases of Zika virus disease. The patients resided in 9 of the 10 municipalities on Yap. Rash, fever, arthralgia, and conjunctivitis were common symptoms. No hospitalizations, hemorrhagic manifestations, or deaths due to Zika virus were reported. We estimated that 73% (95% confidence interval, 68 to 77) of Yap residents 3 years of age or older had been recently infected with Zika virus. Aedes hensilli was the predominant mosquito species identified. This outbreak of Zika virus illness in Micronesia represents transmission of Zika virus outside Africa and Asia. Although most patients had mild illness, clinicians and public health officials should be aware of the risk of further expansion of Zika virus transmission. 2009 Massachusetts Medical Society
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                Author and article information

                Journal
                Healthc Anal (N Y)
                Healthc Anal (N Y)
                Healthcare Analytics (New York, N.y.)
                The Author(s). Published by Elsevier Inc.
                2772-4425
                24 February 2023
                November 2023
                24 February 2023
                : 3
                : 100151
                Affiliations
                [a ]Department of Mathematics, Federal University of Technology, Owerri, Nigeria
                [b ]Abdus Salam School of Mathematical Sciences, Government College University Katchery Road, Lahore 54000, Pakistan
                [c ]Department of Mathematics, Government College University Katchery Road, Lahore 54000, Pakistan
                [d ]Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
                Author notes
                [* ]Corresponding author at: Department of Mathematics, Federal University of Technology, Owerri, Nigeria.
                Article
                S2772-4425(23)00018-7 100151
                10.1016/j.health.2023.100151
                9979858
                36883137
                f4788644-14f9-4b5e-ac3f-921351854f01
                © 2023 The Author(s)

                Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

                History
                : 9 January 2023
                : 16 February 2023
                : 18 February 2023
                Categories
                Article

                co-circulation,backward bifurcation,lyapunov stability,model fitting,optimization

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