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

Abstract

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 , disease mortality , and treatment rate , 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 , and a considerably higher treatment rate , 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 and 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.

Introduction

Co-infections by different pathogens are an increasing area of concern, especially in areas where endemic diseases coincide with global pandemics¹. Leishmaniasis, caused by protozoan parasites of the genus Leishmania and transmitted by sand-flies, is a neglected tropical disease that affects millions worldwide². COVID-19, caused by the novel coronavirus SARS-CoV-2, has taken a deep toll on global health systems^3,4. While both diseases operate through different biological mechanisms, their geographical overlap in high-disease-burden areas increases the possibility of co-infection, raising important questions about combined effects on the immune system and disease severity in co-infected hosts⁵.

The biological interaction of Leishmaniasis and COVID-19 co-infection is complex and largely modulated by their contrasting effects on the immune system. Leishmaniasis is characterised by parasitic invasion of macrophages, leading to disruption of immune regulation and resultant chronic inflammation⁶. COVID-19 causes a hyperactive immune response in severe cases, often leading to a cytokine storm. Co-infection may amplify such immune disturbances, enhancing tissue damage and disease severity. Moreover, immunosuppression due to visceral Leishmaniasis may impede effective immune responses against SARS-CoV-2 and complicate treatment outcomes⁷.

The co-infection context is further complicated by overlapping biological and environmental risk factors. Conditions prevalent in Leishmaniasis-endemic regions, including malnutrition, poverty, and weakened immunity, may increase vulnerability to severe COVID-19⁸. Furthermore, the sand-fly vector of Leishmaniasis is most common in tropical and subtropical climates, the same regions where COVID-19 has had considerable impact. Understanding the biological consequences of this co-infection is important for informing therapeutic interventions and mitigating the combined health burden⁹.

The potential impact of co-infection on healthcare systems is substantial. As illustrated in Fig. 1, Leishmaniasis–COVID-19 co-infection involves overlapping transmission pathways, immune impairment, and compounded disease manifestations that can hinder diagnosis, delay treatment, and elevate mortality risk. Co-infected individuals are therefore likely to require more elaborate management approaches, given the interaction of immune responses and the distinct therapies required by each disease¹⁰. This adds to the resource burden in areas already constrained by Leishmaniasis management needs. Knowledge of such dynamics is essential for informing public health policies on resource optimisation and integrated disease management¹¹.

Fig. 1.

Transmission pathways and health effects of Leishmaniasis–COVID-19 co-infection. Sandfly-mediated transmission of Leishmaniasis involves humans and animal reservoirs, resulting in cutaneous and visceral disease manifestations. When combined with COVID-19, overlapping symptoms and immune impairment can hinder diagnosis, delay treatment, and elevate disease burden and fatality risk.

Mathematical modelling plays a fundamental role in understanding, predicting, and controlling the spread of infectious diseases, providing a rigorous quantitative framework for evaluating intervention strategies such as vaccination, treatment, and vector control^12–19. In particular, compartmental models incorporating stability analysis, sensitivity evaluation, and optimal control have proven indispensable tools for characterising transmission dynamics across a wide range of pathogens, including dengue, Mpox, hepatitis, and emerging respiratory viruses^12–19 Building on this broader methodological foundation, various mathematical models have been developed specifically to study the dynamics of co-infections, offering important insights into how multiple pathogens interact within a shared host population^20–25. Teklu and Mekonnen²⁰ developed and analysed a mathematical model of HIV/AIDS and pneumonia co-infection, examining treatment possibilities at each stage of the disease and deriving effective treatment strategies. Said et al.²¹ performed identifiability analysis of an HIV–Ebola co-infection model using the maximum likelihood estimation method. Amoah-Mensah et al.²² investigated the stability of a mathematical model describing co-infection dynamics between Zika virus and malaria in a malaria-endemic region, advancing our understanding of disease relationships and contributing to preventive strategy development. Said et al.²³ formulated and analysed a compartmental leptospirosis–COVID-19 co-infection model fitted to real data, establishing a methodological precedent for the present work. Slater et al.²⁴ utilised a mathematical model to investigate the interaction between malaria and lymphatic filariasis, shedding light on the population-level dynamics of parasitic co-infections. Ringa et al.²⁵ introduced a mathematical model to study the dynamics of HIV and COVID-19 co-infection, analysing transmission dynamics and optimal control strategies.

Despite this growing body of literature, no prior study has developed a compartmental model that jointly captures the transmission dynamics of COVID-19 and Leishmaniasis with explicit human-vector coupling. Furthermore, existing co-infection models rarely employ data assimilation frameworks such as the Ensemble Kalman Filter (EnKF) to estimate time-varying parameters from real epidemiological data. The present work addresses this gap by: (i) formulating a novel ODE-based co-infection model that integrates bidirectional disease interactions, treatment dynamics, and an explicit sandfly vector population; (ii) applying the EnKF to dynamically estimate model parameters from real-world COVID-19 and Leishmaniasis case data; and (iii) performing short-term forecasting with quantified uncertainty. To the best of our knowledge, this is the first data-driven co-infection modelling study combining these two pathogens.

In this work, we present a nonlinear compartmental model based on ordinary differential equations to study the dynamics of COVID-19 and Leishmaniasis co-infection, with explicit modelling of human and sandfly vector populations. A data assimilation framework using the EnKF is applied to estimate time-evolving model parameters from epidemiological data reports. The model is applied to validate single-disease dynamics, quantify co-infection interactions, and make short-term forecasts.

Model formulation

A nonlinear mathematical model based on ordinary differential equations (ODEs) is developed to study the transmission and progression of COVID-19, Leishmaniasis, and their co-infection. The human population compartments are: susceptible individuals (S); exposed to COVID-19 () or Leishmaniasis (); infectious with COVID-19 (), Leishmaniasis (), or both (); under treatment for COVID-19 () or Leishmaniasis (); and recovered from each (, ). The sandfly vector population includes susceptible (), exposed (), and infectious () vectors.

The model formulation is grounded in the following explicitly stated biological and epidemiological assumptions:

1. The human population is stratified into mutually exclusive compartments based on infection status, with homogeneous mixing assumed within the population.

2. Individuals may contract COVID-19 or Leishmaniasis independently; co-infection is also possible due to overlapping risk factors and immunological vulnerability. This is captured by the bidirectional interaction parameters and .

3. COVID-19 spreads via human-to-human contact (governed by ), whereas Leishmaniasis follows a vector-borne route through infected sandflies (governed by ). Human-to-vector transmission is captured by .

4. Exposed individuals (, ) progress to the infectious stage at disease-specific rates, reflecting the incubation periods of each disease.

5. Co-infected individuals () experience elevated disease burden and mortality compared to singly infected individuals. The co-infection-induced mortality rate is assumed higher than the single-disease mortality rates and , consistent with clinical evidence of compounded immunological disruption.

6. Treatment compartments (, ) capture the effects of therapeutic intervention. Treated individuals may either recover or die; transition rates are derived from observed clinical dynamics. Lower treatment rates in the co-infection model compared to sub-models reflect possible healthcare access delays or difficulty in distinguishing overlapping symptoms.

7. Recovery provides temporary immunity within the model’s time frame; recovered individuals (, ) may lose immunity at rates and and return to the susceptible class.

8. The sandfly vector population is modeled with susceptible (), (E_v) exposed, and infected () compartments; vector infection occurs only through contact with infectious human hosts ( and ), consistent with Leishmaniasis transmission biology.

The complete model structure is illustrated schematically in Fig. 2, which presents the flowchart of all compartments and transition pathways of the co-infection model, including human-to-human COVID-19 transmission, vector-mediated Leishmaniasis transmission, and bidirectional co-infection interactions. The governing ODE system is given in model (1); parameter descriptions are summarized in Table 1.

1

Fig. 2.

Schematic diagram of the co-infection model. All compartments and transition pathways are shown, including human-to-human COVID-19 transmission (via ), vector-mediated Leishmaniasis transmission (via , ), bidirectional co-infection enhancement rates (, ), treatment flows (, ), and recovery pathways (, , , ).

Table 1.

Model parameters and their biological interpretations for the Leishmaniasis–COVID-19 co-infection system.

Parameter	Biological meaning
Λ	Recruitment rate into the human population
μ	Natural mortality rate of humans
	COVID-19–induced mortality rate
	Leishmaniasis-induced mortality rate
	Disease-induced mortality rate for co-infected individuals
	Mortality rate among individuals under COVID-19 treatment
	Mortality rate among individuals under Leishmaniasis treatment
	Effective transmission rate of COVID-19 among humans
	Transmission rate of Leishmaniasis from infectious vectors to susceptible humans
	Rate of acquiring Leishmaniasis by individuals infected with COVID-19
	Rate of acquiring COVID-19 by individuals infected with Leishmaniasis
	Biting rate of sandflies on susceptible humans
	Biting rate of sandflies on Leishmaniasis-infected humans
	Progression rate from exposed to infectious COVID-19 class
	Progression rate from exposed to infectious Leishmaniasis class
	Progression rate from exposed to infectious vector class
	Recovery rate of COVID-19-infected individuals
	Recovery rate of Leishmaniasis-infected individuals
	Recovery rate from COVID-19 for co-infected individuals
	Recovery rate from Leishmaniasis for co-infected individuals
	Treatment initiation rate for COVID-19-infected individuals
	Treatment initiation rate for Leishmaniasis-infected individuals
	Recovery rate of individuals treated for COVID-19
	Recovery rate of individuals treated for Leishmaniasis
	Rate of loss of immunity to COVID-19
	Rate of loss of immunity to Leishmaniasis
π	Recruitment rate of the sandfly vector population
	Transmission rate of Leishmaniasis from infected humans to susceptible vectors
	Natural mortality rate of the vector population

Ensemble Kalman filter for parameter estimation

The Ensemble Kalman Filter (EnKF) is a sequential data assimilation technique that combines model predictions with observed data to estimate both the state and parameters of nonlinear systems^26,27. Unlike the traditional Kalman Filter, which assumes linear dynamics, or the Extended Kalman Filter, which uses linear approximations, the EnKF employs an ensemble of state realisations to compute error statistics, making it particularly suitable for nonlinear and high-dimensional epidemiological models^28–30.

Let the augmented state vector be defined as

where the state sub-vector

contains all compartmental state variables, and the parameter sub-vector

contains all unknown model parameters to be estimated. Here the superscript denotes the vector transpose, indicating that although each sub-vector is written as a row for typographical convenience, it is treated as a column vector in all subsequent matrix operations.

Ensemble initialisation. An ensemble of N = 100 members is initialised. Each state variable is initialised from a distribution consistent with reported epidemiological data at t = 0 (e.g. reported case counts for , , , with the susceptible pool inferred from the total population). Unknown parameters are initialised from uniform distributions over biologically plausible ranges: e.g. ; ; .

Forecast step. At each time step k, each ensemble member is propagated forward using the model dynamics:

where is the model operator and denotes process noise. Process noise is injected into the parameter components at each step to prevent ensemble collapse and allow parameters to evolve over time; the process noise covariance is diagonal with small variance for each parameter.

Observation function. Predicted observations for each ensemble member are computed as:

where maps the augmented state to the observable quantities, i.e. the monthly reported case counts for , , and . Observation noise is assumed Gaussian with zero mean and covariance , where the standard deviations are set proportional to the observed case counts to reflect reporting uncertainty.

Analysis step. The ensemble means are

The cross-covariance and observation covariance are

The Kalman gain matrix is

Finally, each ensemble member is updated using the actual observation :

This procedure is repeated iteratively at each monthly observation time-point, enabling joint estimation of state trajectories and time-varying parameters.

Results

This section presents simulation results for the COVID-19-only sub-model, the Leishmaniasis-only sub-model, and the full co-infection model. Individual sub-model simulations were run over 12 months; the co-infection model was fitted to three independent 6-month datasets. The EnKF was applied throughout for parameter estimation and state updating. Mean parameter values are reported in Tables 2, 3 and 4.

Table 2.

Values of model parameters with units and sources.

Parameter	Value	Unit	Source
Λ	–		Estimated31,32
μ	–		Estimated33
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	–		Estimated (fitting)
	0.8600		34
	0.7000		35
	0.0300		35
	0.0100		36
	0.0100		36
	0.0019		23
	0.0022		23
	0.0059		37
	0.0250		35
	0.9629		38
	0.0064		39
π	8.2300		35
	0.0100		35

Table 3.

Estimated parameter values for the COVID-19 and Leishmaniasis sub-models using two different 12-month datasets.

	Parameter	Estimated value	C.I
COVID-19		0.2451	(0.2193-0.3134)
		0.0067	(0.0015-0.0324)
		0.0142	(0.0097-0.0782)
		0.0075	(0.0016-0.0120)
		0.0714	(0.0539-0.0916)
Leishmaniasis		0.2319	(0.1039-0.3521)
		0.0041	(0.0011-0.0210)
		0.0721	(0.0021-0.0976)
		0.0013	(0.0009-0.0109)
		0.0613	(0.0413-0.0896)
		0.0004	(0.0001-0.0007)

Table 4.

Model parameter estimates using three different observational 6-month datasets.

	Parameter	Estimated value	C.I
COVID-19		0.2806	(0.2193-0.3134)
		0.0031	(0.0015-0.0324)
		0.0643	(0.0097-0.0782)
		0.0045	(0.0016-0.0120)
Leishmaniasis		0.2204	(0.1039-0.3521)
		0.0033	(0.0011-0.0210)
		0.0380	(0.0021-0.0976)
		0.0012	(0.0009-0.0109)
Co-infection		0.3624	(0.3124-0.4312)
		0.3394	(0.3013-0.4127)
		0.0060	(0.0050-0.0070)

In the COVID-19-only sub-model, the EnKF estimated a transmission rate , consistent with community-level SARS-CoV-2 transmission in similar settings and reflecting the airborne nature of the pathogen. The disease-induced mortality rate reflects a measurable mortality burden among untreated individuals, consistent with reported COVID-19 case-fatality rates in resource-limited settings. The treatment initiation rate is relatively low, suggesting possible delays or limitations in healthcare access or diagnosis. The death rate among treated individuals, , is slightly higher than , which may reflect late-stage treatment initiation or comorbidities. The recovery rate of treated individuals, , indicates a positive therapeutic response: patients under clinical care are substantially more likely to recover than to die. Temporal evolution of these parameters is illustrated in Figs. 3, 4, 5 and 6.

Fig. 3.

Model fitting of COVID-19 data using the Ensemble Kalman Filter (EnKF) approach. The observed data points are shown alongside the model predictions, with the shaded region representing the 95% confidence interval. The EnKF enables real-time parameter estimation and state correction, capturing the stochastic variability in disease progression.

Fig. 4.

Monthly variation in estimated parameters , and , over a 12-month period.

Fig. 5.

Monthly variation in estimated parameters , and over a 12-month period.

Fig. 6.

Monthly variation in estimated parameter over a 12-month period.

In the Leishmaniasis-only sub-model, the estimated transmission rate reflects a sustained but moderate disease spread, consistent with the vector-dependent nature of Leishmaniasis. The disease-induced mortality rate for untreated individuals, , is lower than that of COVID-19, likely reflecting a more chronic and slower-progressing disease course. The higher treatment rate suggests better case detection or treatment compliance for Leishmaniasis in the studied population compared to COVID-19. The very low mortality among treated individuals, , highlights the efficacy of available antileishmanial therapies. The recovery rate confirms favourable clinical outcomes under treatment. The estimated human-to-vector transmission rate, , is very low, reflecting ecological constraints on sandfly infection. Temporal parameter trends are illustrated in Figs. 7, 8, 9 and 10.

Fig. 7.

Model fitting of Leishmaniasis data using the Ensemble Kalman Filter (EnKF) approach. The observed data points are shown alongside the model predictions, with the shaded region representing the 95% confidence interval.

Fig. 8.

Monthly variation in estimated parameters , over a 12-month period.

Fig. 9.

Monthly variation in estimated parameters , and . over a 12-month period.

Fig. 10.

Monthly variation in estimated parameters , and over a 12-month period.

The parameter estimation for the full co-infection model reveals important insights into the joint disease dynamics. The COVID-19 transmission rate was estimated at , slightly elevated compared to the sub-model, possibly reflecting increased host susceptibility or behavioural mixing under co-infection conditions. For Leishmaniasis, , slightly reduced, which may reflect reporting effects or interaction-induced suppression.

The interaction parameters and quantify the bidirectional synergy of co-infection. Specifically, represents the elevated rate at which COVID-19-infected individuals acquire Leishmaniasis: SARS-CoV-2 causes profound immune dysregulation (cytokine storms, lymphopenia) that reduces the host’s ability to control Leishmania infection. Conversely, represents the elevated risk of COVID-19 acquisition for Leishmaniasis-infected individuals, driven by the macrophage-mediated immunosuppression characteristic of visceral Leishmaniasis, which impairs innate antiviral defences. Both values () are substantially higher than the primary transmission rates (), confirming that co-infection significantly amplifies transmission risk for both pathogens. The co-infection-induced mortality rate is higher than either single-disease mortality rate, underscoring the compounded health risk for co-infected individuals.

Data fitting results across the three datasets are shown in Figs. 11, 12 and 13, demonstrating strong agreement between model predictions and observed case counts. Parameter evolution plots (Figs. 14, 15, 16, 17 and 18) confirm temporally heterogeneous dynamics. Ensemble heat-maps (Figs. 19, 20, 21, 22 and 23) show progressive narrowing of the ensemble spread, indicating improved parameter confidence as data are assimilated. Three-month forecasts are shown in Figs. 24, 25 and 26; widening confidence intervals in the forecast period are expected and reflect the absence of new observational data.

Fig. 11.

Model fitting of the COVID-19 infectious population over a six-month period using the Ensemble Kalman Filter (EnKF). The black curve represents the mean prediction from the EnKF based on the evolving ensemble of system states. The blue shaded region denotes the 95% confidence interval, capturing uncertainty in the model estimates. Triangle markers correspond to the observed data points used for data assimilation. The results demonstrate the EnKF’s effectiveness in capturing the temporal trends of the COVID-19 epidemic under uncertainty.

Fig. 12.

Model fitting of the Leishmaniasis infectious population over a six-month period using the Ensemble Kalman Filter (EnKF). The mean EnKF prediction is shown as a black curve, while the 95% confidence interval is illustrated with a blue shaded region. Observed case data are represented by triangle markers. This figure highlights the EnKF’s ability to assimilate noisy data and produce a probabilistic estimate of disease progression for a neglected tropical disease.

Fig. 13.

Model fitting of the co-infected population (individuals simultaneously infected with both COVID-19 and Leishmaniasis) over six months using the Ensemble Kalman Filter (EnKF). The black line indicates the EnKF mean estimate, while the surrounding blue shaded region represents the 95% confidence interval. Observational data points are shown as triangle markers. The results illustrate the EnKF’s capacity to capture the interactions between co-circulating infections and infer latent epidemic behavior under uncertainty.

Fig. 14.

Monthly variation in estimated parameters , and over a 6-month period.

Fig. 15.

Monthly variation in estimated parameters , and over a 6-month period.

Fig. 16.

Monthly variation in estimated parameters , and over a 6-month period.

Fig. 17.

Monthly variation in estimated parameters , and over a 6-month period.

Fig. 18.

Monthly variation in estimated parameters , , and over a 6-month period.

Fig. 19.

Heat-map visualization of the temporal evolution and ensemble diversity for each estimated parameter ( and ) across all time steps. Each subplot corresponds to a specific parameter and displays its values for 100 ensemble members over 6 months. Color intensity indicates the magnitude of the parameter estimates. This confirms parameter variability and dynamic tracking throughout the Ensemble Kalman Filter process.

Fig. 20.

Heat-map visualization of the temporal evolution and ensemble diversity for each estimated parameter ( and ) across all time steps. Each subplot corresponds to a specific parameter and displays its values for 100 ensemble members over 6 months. Color intensity indicates the magnitude of the parameter estimates. This confirms parameter variability and dynamic tracking throughout the Ensemble Kalman Filter process.

Fig. 21.

Heat-map visualization of the temporal evolution and ensemble diversity for each estimated parameter ( and ) across all time steps. Each subplot corresponds to a specific parameter and displays its values for 100 ensemble members over 6 months. Color intensity indicates the magnitude of the parameter estimates. This confirms parameter variability and dynamic tracking throughout the Ensemble Kalman Filter process.

Fig. 22.

Heat-map visualization of the temporal evolution and ensemble diversity for each estimated parameter ( and ) across all time steps. Each subplot corresponds to a specific parameter and displays its values for 100 ensemble members over 6 months. Color intensity indicates the magnitude of the parameter estimates. This confirms parameters variability and dynamic tracking throughout the Ensemble Kalman Filter process.

Fig. 23.

Heat-map visualization of the temporal evolution and ensemble diversity for each estimated parameter (, and ) across all time steps. Each subplot corresponds to a specific parameter and displays its values for 100 ensemble members over 6 months. Color intensity indicates the magnitude of the parameter estimates. This confirms parameter variability and dynamic tracking throughout the Ensemble Kalman Filter process.

Fig. 24.

Three-month ahead forecast of COVID-19 () cases using the Ensemble Kalman Filter (EnKF). The plot shows fitted values during the observed period and projected values with 95% confidence intervals beyond the fitting horizon.

Fig. 25.

Three-month ahead forecast of Leishmaniasis () cases using the EnKF-based model. The shaded region indicates the 95% confidence interval of the forecasted values.

Fig. 26.

Forecast of co-infection () cases for the next three months. The plot displays both historical fit and predictive mean with confidence bounds, highlighting the expected dynamics under current parameter estimates.

Discussion

The simulation results offer important insights into the transmission dynamics of COVID-19 and Leishmaniasis, both individually and as a co-infection system. The application of the EnKF enabled dynamic estimation of key epidemiological parameters while accounting for uncertainty in real data. Individual sub-model validation over 12 months provided a solid foundation for the co-infection analysis. The strong agreement between observations and predictions confirms the model structure and estimation framework.

In the COVID-19 sub-model, the estimated is consistent with community-level SARS-CoV-2 spread. The relatively slow treatment initiation rate () may reflect diagnostic delays or healthcare access barriers. In contrast, the The leishmaniasis sub-model showed a higher treatment rate (), suggesting a more efficient clinical response to this disease in the modelled setting. The lower mortality among Leishmaniasis-treated individuals () highlight effective antileishmanial therapy. These differences reflect fundamentally distinct transmission mechanisms and disease management realities: COVID-19 requires rapid response to prevent large-scale community outbreaks, while Leishmaniasis control relies more heavily on vector control and sustained treatment access.

The co-infection analysis revealed that the simultaneous presence of both diseases significantly alters transmission and clinical dynamics. The elevated in the co-infection model may reflect heightened susceptibility due to immunosuppression, while the slightly lower may result from under-reporting or interaction-induced suppression of Leishmaniasis spread. The high values of and confirm a strong bidirectional synergy. The higher co-infection mortality rate () compared to single-disease rates underscores the compounded clinical risk.

These findings carry several important implications for public health practice. First, the high values of the interaction parameters () indicate that in co-endemic settings, the presence of either disease substantially elevates the risk of the other. This calls for integrated co-infection surveillance systems capable of simultaneously tracking and reporting both diseases and flagging at-risk individuals. Second, resource allocation strategies in Leishmaniasis-endemic regions must account for the potential for COVID-19 co-infection, which may require additional clinical resources (intensive care, combined diagnostic protocols). Third, the higher mortality in co-infected individuals argues for prioritising this group in triage and treatment protocols. Fourth, the success of the EnKF framework in dynamically tracking parameter changes demonstrates its value for real-time epidemic monitoring; health authorities could use such adaptive models to update disease projections as new surveillance data becomes available. Finally, the differing treatment dynamics between the two diseases (faster uptake for Leishmaniasis, slower for COVID-19) suggest that different intervention priorities are needed: COVID-19 management should emphasise early detection and rapid clinical referral, while Leishmaniasis control should maintain strong vector control programmes and sustained access to antileishmanial therapies.

Conclusion

This study presents a comprehensive modelling framework to analyse the transmission dynamics of COVID-19 and Leishmaniasis, both individually and as a co-infection system, using the Ensemble Kalman Filter for dynamic parameter estimation. Sub-model simulations provided a clear epidemiological characterisation of each disease, while the co-infection model revealed critical interaction effects that alter transmission rates and clinical outcomes. The quantitative agreement between model projections and observed data confirms both the model structure and the capacity of the EnKF to infer time-varying disease dynamics from real-world data.

Significant differences in transmission mechanisms, mortality rates, and treatment dynamics were identified between the two diseases. COVID-19’s direct human-to-human transmission and low treatment uptake necessitate rapid response interventions, while Leishmaniasis’ vector-borne nature and favourable treatment outcomes underscore the importance of persistent vector control and treatment access. Under co-infection, the bidirectional interaction parameters and indicate significant mutual amplification of transmission risk and mortality, requiring comprehensive clinical management.

The findings underscore the importance of integrated disease surveillance in co-endemic regions, and the successful application of the EnKF demonstrates the value of adaptive data assimilation for real-time epidemic monitoring. These insights contribute to a more nuanced understanding of multi-pathogen epidemics and can inform holistic public health responses and resource allocation policies.

Author contributions

M.S. (Muhammad Said) conceived the study, developed the mathematical model, implemented the Ensemble Kalman Filter (EnKF) algorithm, performed the formal analysis and numerical simulations, and drafted the original manuscript. M.A.S. (Mussa A. Stephano) contributed to data collection, model validation, interpretation of results, and assisted in manuscript preparation and revision. I.H.J. (Il Hyo Jung) supervised the research, contributed to conceptual refinement and methodological design, and critically revised the manuscript for important intellectual content. All authors reviewed the manuscript and approved the final version.

Funding

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIT) (No. RS-2024-00342113 and RS-2022-NR070839).

Data availability

The data used in this study consist of aggregated, publicly available epidemiological records. COVID-19 case data were obtained from the online database https://www.coronaboard.com . Leishmaniasis-related data were derived from aggregated epidemiological records reported in Hashemi et al., An eco-epidemiological study of cutaneous leishmaniasis in Dezful, Iran, during 2004–2011, published in the Journal of Occupational Health and Epidemiology and accessible via the DOI https://doi.org/10.18869/acadpub.johe.3.1.45 . No individual-level or identifiable human data were used in this study.

Declarations

Competing interests

The authors declare no competing interests.