EPIDEMIOLOGICAL MODELING WITH DEVELOPING COUNTRIES REALITIES: APPLICATION TO EBOLA AND COVID SPREAD

Abdon Atangana and Seda Igret Araz
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Abdon Atangana: Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa†Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan‡IT4Innovations, VSB — Technical University of Ostrava, Ostrava-Poruba, Czech Republic
Seda Igret Araz: �Department of Mathematics Education, Siirt University, Siirt, Turkey

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-28

Abstract: In this paper, we introduced two approaches that will help mathematical models not only to accurately present future impact of a given outbreak, but also to consider challenges faced by undeveloped countries, indeed this methodology is also important even in developed countries. The first approach was to construct indicator rate functions representing death, recoveries and infection rates using collected data. The second approach is to include into the new mathematical model, undetected classes for death, infected and recoveries. The paper presents a critical analysis of epidemiological modeling of infectious disease with a particular application to Ebola and COVID-19 spread. To achieve our goal, we question the current approach to the model spread of infectious diseases in general. We suggested a novel methodology that could be more accurate than the existing one, by introducing into the mathematical conceptual model undetected classes. We presented a detailed analysis of these models including their well-posedness and numerical solutions. We considered the spread of two different infectious diseases Ebola and COVID-19. Existing mathematical models of both, the modifications suggested in this work were compared with experimental data for Ebola in Congo and COVID-19 in South Africa. The comparison showed that the suggested methodology is more informative than the existing one as it helps predict infected, recovered, and dead classes considering the realities of undeveloped countries. We strongly believe that this new approach will help mathematicians model more accurately the spread of infectious diseases. Thus having better predictions, results will help law makers to take decisions that will help countries, governments and cemeteries to reduce the burdens due to the impact of an outbreak.

Keywords: Epidemiology; Rate Indicator Function; Future Prediction; Fractional Calculus (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401176

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