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      Fractional-order dynamics of Chagas-HIV epidemic model with different fractional operators

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          Abstract

          <abstract><p>In this research, we reformulate and analyze a co-infection model consisting of Chagas and HIV epidemics. The basic reproduction number \(R_0 \) of the proposed model is established along with the feasible region and disease-free equilibrium point \(E^0 \). We prove that \(E^0 \) is locally asymptotically stable when \(R_0 \) is less than one. Then, the model is fractionalized by using some important fractional derivatives in the Caputo sense. The analysis of the existence and uniqueness of the solution along with Ulam-Hyers stability is established. Finally, we solve the proposed epidemic model by using a novel numerical scheme, which is generated by Newton polynomials. The given model is numerically solved by considering some other fractional derivatives like Caputo, Caputo-Fabrizio and fractal-fractional with power law, exponential decay and Mittag-Leffler kernels.</p></abstract>

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          Most cited references31

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          Is Open Access

          The impact of Chagas disease control in Latin America: a review

          Discovered in 1909, Chagas disease was progressively shown to be widespread throughout Latin America, affecting millions of rural people with a high impact on morbidity and mortality. With no vaccine or specific treatment available for large-scale public health interventions, the main control strategy relies on prevention of transmission, principally by eliminating the domestic insect vectors and control of transmission by blood transfusion. Vector control activities began in the 1940s, initially by means of housing improvement and then through insecticide spraying following successful field trials in Brazil (Bambui Research Centre), with similar results soon reproduced in São Paulo, Argentina, Venezuela and Chile. But national control programmes only began to be implemented after the 1970s, when technical questions were overcome and the scientific demonstration of the high social impact of Chagas disease was used to encourage political determination in favour of national campaigns (mainly in Brazil). Similarly, large-scale screening of infected blood donors in Latin America only began in the 1980s following the emergence of AIDS. By the end of the last century it became clear that continuous control in contiguous endemic areas could lead to the elimination of the most highly domestic vector populations - especially Triatoma infestans and Rhodnius prolixus - as well as substantial reductions of other widespread species such as T. brasiliensis, T. sordida, and T. dimidiata, leading in turn to interruption of disease transmission to rural people. The social impact of Chagas disease control can now be readily demonstrated by the disappearance of acute cases and of new infections in younger age groups, as well as progressive reductions of mortality and morbidity rates in controlled areas. In economic terms, the cost-benefit relationship between intervention (insecticide spraying, serology in blood banks) and the reduction of Chagas disease (in terms of medical and social care and improved productivity) is highly positive. Effective control of Chagas disease is now seen as an attainable goal that depends primarily on maintaining political will, so that the major constraints involve problems associated with the decentralisation of public health services and the progressive political disinterest in Chagas disease. Counterbalancing this are the political and technical cooperation strategies such as the "Southern Cone Initiative" launched in 1991. This international approach, coordinated by PAHO, has been highly successful, already reaching elimination of Chagas disease transmission in Uruguay, Chile, and large parts of Brazil and Argentina. The Southern Cone Initiative also helped to stimulate control campaigns in other countries of the region (Paraguay, Bolivia, Peru) which have also reached tangible regional successes. This model of international activity has been shown to be feasible and effective, with similar initiatives developed since 1997 in the Andean Region and in Central America. At present, Mexico and the Amazon Region remain as the next major challenges. With consolidation of operational programmes in all endemic countries, the future focus will be on epidemiological surveillance and care of those people already infected. In political terms, the control of Chagas disease in Latin America can be considered, so far, as a victory for international scientific cooperation, but will require continuing political commitment for sustained success.
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            Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties

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              Manifestations of Chagas disease (American trypanosomiasis) in patients with HIV/AIDS.

              Between June 1989 and December 2005, an observational study of adults co-infected with HIV and Trypanosoma cruzi was conducted, to investigate the spectrum of manifestations of chronic Chagas disease (American trypanosomiasis) in the HIV-positive. The 31 men and 22 women investigated were aged 23-59 years. Each subject was investigated by ambulatory (Holter) and non-ambulatory electrocardiography, chest X-ray, oesophagography and echocardiography (to determine the clinical form of trypanosomiasis), by xenodiagnosis, blood culture and the microscopical examination of blood (to explore their T. cruzi parasitaemia), and by counting their CD4 T cells (to stage their HIV infection). The subjects were followed-up for 1-190 months (median = 58 months) and checked for re-activation of their Chagas disease, which was usually defined by the occurrence of unusual clinical manifestations and/or the detection, by microscopical examination, of trypanosomes in the blood or cerebrospinal fluid. Eleven (20.8%) of the subjects showed re-activation, another nine (17.0%) were found to have developed high T. cruzi parasitaemias but these were only detected by xenodiagnosis or culture, and 15 (28.3%) had illnesses typical of chronic Chagas disease in HIV-negative individuals, with low parasitaemias. Anti-T. cruzi therapy (benznidazole), recommended for 17 patients, resulted in the sustained reduction of parasitaemia in 11 of the 12 subjects who completed treatment. Chagas disease was the cause of death of eight of the 14 subjects who died during the study. Four of the women investigated gave birth, each to a single child, during follow-up, and three of the four babies showed evidence of the congenital transmission of T. cruzi.
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                Author and article information

                Journal
                AIMS Mathematics
                MATH
                American Institute of Mathematical Sciences (AIMS)
                2473-6988
                2022
                2022
                : 7
                : 10
                : 18897-18924
                Affiliations
                [1 ]Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan
                [2 ]Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan
                [3 ]Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
                [4 ]Institute for the Future of Knowledge, University of Johannesburg, P.O. Box 524, Auckland Park 2006, South Africa
                Article
                10.3934/math.20221041
                3598f6aa-acef-4933-9f0f-132adce0b5bc
                © 2022
                History

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