INTRODUCTION: This work focuses on the Dengue-viremia ABC (Atangana-Baleanu Caputo) fractional-order differential equations, accounting for both symptomatic and asymptomatic infected cases. Symptomatic cases are characterized by higher viremia levels, whereas asymptomatic cases exhibit lower viremia levels. The fractional-order model highlights memory effects and other advantages over traditional models, offering a more comprehensive representation of dengue dynamics. METHODS: The total population is divided into four compartments: susceptible, asymptomatic infected, symptomatic infected, and recovered. The model incorporates an immune-boosting factor for asymptomatic infected individuals and clinical treatment for symptomatic cases. Positivity and boundedness of the model are validated, and both local and global stability analyses are performed. The novel Adams-Bash numerical scheme is utilized for simulations to rigorously assess the impact of optimal control interventions. RESULTS: The results demonstrate the effectiveness of the proposed control strategies. The reproduction numbers must be reduced based on specific optimal control conditions to effectively mitigate disease outbreaks. Numerical simulations confirm that the optimal control measures can significantly reduce the spread of the disease. DISCUSSION: This research advances the understanding of Dengue-viremia dynamics and provides valuable insights into the application of ABC fractional-order analysis. By incorporating immune-boosting and clinical treatment into the model, the study offers practical guidelines for implementing successful disease control strategies. The findings highlight the potential of using optimal control techniques in public health interventions to manage disease outbreaks more effectively.

Department of Machining Assembly and Engineering Metrology Faculty of Mechanical Engineering VSB Technical University of Ostrava Ostrava Czechia

Department of Mathematics Vel Tech Rangarajan Dr Sagunthala R and D Institute of Science and Technology Chennai Tamil Nadu India

Department of Mechanical Engineering Vel Tech Rangarajan Dr Sagunthala R and D Institute of Science and Technology Chennai Tamil Nadu India

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World Health Organization . Epidemiology (WHO). (2021). https://www.whho.int/denguecontrol/disease/en/2021

Kautner I, Robinson MJ, Kuhnle U. Dengue virus infection: epidemiology, pathogenesis, clinical presentation, diagnosis, and prevention. J Pediatr. (1997) 131:516–24. 10.1016/S0022-3476(97)70054-4 PubMed DOI

Gubler DJ. Epidemic dengue/dengue hemorrhagic fever as a public health, social and economic problem in the 21st century. Trends Microbiol. (2002) 10:100–3. 10.1016/S0966-842X(01)02288-0 PubMed DOI

Esteva L, Vargas C. Analysis of a dengue disease transmission model. Math Biosci. (1998) 150:131–51. 10.1016/S0025-5564(98)10003-2 PubMed DOI

Esteva L, Vargas C. A model for dengue disease with variable human population. J Math Biol. (1999) 38:220–40. 10.1007/s002850050147 PubMed DOI

Feng Z, Velasco-Hernández JX. Competitive exclusion in a vector-host model for the dengue fever. J Math Biol. (1997) 35:523–44. 10.1007/s002850050064 PubMed DOI

Owolabi KM, Atangana A. Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative. Chaos, Solitons Fractals. (2017) 105:111–9. 10.1016/j.chaos.2017.10.020 PubMed DOI

Pongsumpun P. Mathematical model of dengue disease with the incubation period of virus. World Acad Sci Eng Technol. (2008) 44:328–32.

Pinho STRD, Ferreira CP, Esteva L, Barreto FR, Morato e Silva VC, Teixeira MGL. Modelling the dynamics of dengue real epidemics. Philosoph Trans Royal Soc A: Mathem Phys Eng Sci. (2010) 368:5679–93. 10.1098/rsta.2010.0278 PubMed DOI

Kongnuy R. Mathematical modeling for dengue transmission with the effect of season. Int J Biol Med Sci. (2010) 5:74–8. 10.5281/zenodo.1327917 DOI

Side S, Noorani SM. A SIR model for spread of dengue fever disease (simulation for South Sulawesi, Indonesia and Selangor, Malaysia). World J Model Simul. (2013) 9:96–105. 10.13140/RG.2.1.5042.6721 DOI

Gakkhar S, Chavda NC. Impact of awareness on the spread of dengue infection in human population. Appl Math. (2013) 4:142–7. 10.4236/am.2013.48A020 DOI

Diethelm K, Ford NJ. Analysis of fractional differential equations. J Math Anal Appl. (2002) 265:229–48. 10.1006/jmaa.2000.7194 DOI

Soewono E, Supriatna AK. A two-dimensional model for the transmission of dengue fever disease. Bullet Malaysian Mathem Sci Soc. (2001) 24:1.

Jan R, Khan MA, Kumam P, Thounthong P. Modeling the transmission of dengue infection through fractional derivatives. Chaos, Solitons Fractals. (2019) 127:189–216. 10.1016/j.chaos.2019.07.002 DOI

Caputo M, Fabrizio M. A new definition of fractional derivative without singular kernel. Prog Fract Different Appl. (2015) 1:73–85. 10.12785/pfda/010201 DOI

Fatmawati Khan MA, Alfiniyah C, Alzahrani E. Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator. Adv. Diff. Equat. (2020) 2020:422. 10.1186/s13662-020-02881-w DOI

Boulaaras S, Kan R. Dynamical analysis of the transmission of dengue fever via caputo – fabrizio fractional derivative. Chaos, Solitons Fractals. (2022) 2022:100072. 10.1016/j.csfx.2022.100072 DOI

Sanusi W, Badwi N, Zaki A, Sidjara S, Sari N, Pratama MI, et al. . Analysis and simulation of SIRS model for dengue fever transmission in South Sulawesi, Indonesia. J Appl Mathem. (2021) 2021:1–8. 10.1155/2021/2918080 DOI

Ahmad S, Javeed S, Ahmad H, Khushi J, Elagan SK, Khames A. Analysis numerical solution of novel fractional model for dengue. Results Physics. (2021) 28:104669. 10.1016/j.rinp.2021.104669 DOI

Nur W, Rachman H, Abdal NM, Abdy M, Side S. SIR model analysis for transmission of dengue fever disease with climate factors using lyapunov function. J Phys. . (2018) 1028:012117. 10.1088/1742-6596/1028/1/012117 DOI

Khan MA. Dengue infection modeling and its optimal control analysis in East Java, Indonesia. Heliyon. (2021) 7:1. 10.1016/j.heliyon.2021.e06023 PubMed DOI PMC

Bonyah E, Juga ML, Chukwu CW. A fractional order dengue fever model in the context of protected travelers. Alexandria Eng J. (2022) 61:927–36. 10.1016/j.aej.2021.04.070 DOI

Khan FM, Khan ZU, Lv YP, Yusuf A, Din A. Investigating of fractional order dengue epidemic model with ABC operator. Results Physics. (2021) 24:104075. 10.1016/j.rinp.2021.104075 DOI

Agarwal P, Singh R, ul Rehman A. Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam–Bashforth–Moulton predictor-corrector scheme. Chaos, Solitons and Fractals. (2021) 143:110564. 10.1016/j.chaos.2020.110564 DOI

Anggriani N, Supriatna AK, Soewono E. A critical protection level derived from dengue infection mathematical model considering asymptomatic and symptomatic classes. J Phys. (2013) 423:012056. 10.1088/1742-6596/423/1/012056 DOI

Jan R, Khan MA, Gómez-Aguilar JF. Asymptomatic carriers in transmission dynamics of dengue with control interventions. Optimal Cont Appl Meth. (2020) 41:430–47. 10.1002/oca.2551 DOI

Vijayalakshmi GM, Ariyanatchi M. Adams–Bashforth Moulton numerical approach on dengue fractional atangana baleanu caputo model and stability analysis. Int J Appl Comput Mathem. (2024) 10:32. 10.1007/s40819-023-01652-x DOI