Epidemiological modeling of Influenza-Like Illness (ILI) transmission in Jakarta, Indonesia through cumulative generating operator on SLIR model

Influenza-Like Illness (ILI) constitutes a significant global health concern characterized by its high infection rates and widespread distribution worldwide. While influenza viruses, primarily types A and B, are primary contributors to ILI cases, other respiratory viruses also play a role in its prevalence. Jakarta, Indonesia’s largest and densely populated city, has consistently reported a notable weekly number of ILI cases from 2016 to mid-2022. Intriguingly, this pattern of cases is irregular and does not exhibit a direct association with seasonal climate fluctuations. In response to this complex scenario, we have developed a SLIR mathematical model featuring a cumulative generating operator in the form of a multiple-terms sigmoid function, obtained from weekly cumulative data to derive model solutions. A total of 12 terms within the sigmoid function yielded a decent fit to the actual data spanning 339 weeks. Our correlation analysis unveiled distinct temporal relationships within the model, revealing an 8-week time lag between the dynamics of the infection rate and the latent compartment, along with a 2-week lag marking the incubation period between the latent and infected compartments. Furthermore, the effective reproduction number displayed recurrent fluctuations around a threshold of 1, indicating the endemic characteristics where infection persists within the population. This in-depth comprehension of ILI transmission dynamics and effective reproduction numbers plays a significant role in devising control measures and informed policy-making decisions.