A data-driven analysis and forecasting of Leishmaniasis-COVID-19 co-infection model using ensemble Kalman filter

Co-infections involving viruses and parasites pose a major concern for global health, particularly in areas where both infections are endemic. In this paper, we present a co-infection epidemic model that considers the transmission dynamics of COVID-19 and leishmaniasis among human and vector populations. The model is developed based on considering the specific latency periods of each infection, treatment, recovery, reinfection, and cross-infection process. The Ensemble Kalman Filter technique is applied to estimate the key model’s parameters using real data, incorporating temporal variation and uncertainty in disease transmission and progression. The model is first divided into COVID-19-only and leishmaniasis-only sub-models to validate the dynamics of each disease over 12 months. For the COVID-19 sub-model, several important estimated parameters include transmission rate \(β _1 = 0.2451\) , disease mortality \(μ _1 = 0.0067\) , and treatment rate \(α _1 = 0.0142\) , indicating a relatively slow response to disease treatments and moderate disease severity. On the other hand, the Leishmaniasis model had a slightly lower transmission rate \(β _2 = 0.2319\) , and a considerably higher treatment rate \(α _2 = 0.0721\) , implying more efficient case management of the vector-borne disease. The complete model for co-infection, estimated from three groups of six months of data, exhibits synergistic effects through interaction parameters \(δ _1 = 0.3624\) and \(δ _2= 0.3394\) that reflect a higher likelihood of acquiring another disease while already infected with the first. The model predictions were highly consistent with observed data, and the estimated parameters show significant temporal variability. Projections over a three-month horizon demonstrated strong predictive performance. These results underscore the need for an integrated surveillance and control framework for co-endemic disease management.