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Open research questions in Mathematical and Theoretical Epidemiology and Ecology Models

81 unresolved questions extracted from the limitations and future-work sections of 441 Mathematical and Theoretical Epidemiology and Ecology Models papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • Future research can focus on estimating the parameters of the model from real data. The model can be extended to consider more complex scenarios. The results of the paper can be used to inform public health policy.

    Mathematical Modeling for the Spread and Control of Infectious Diseases by Spread of Awareness in Human Population · 2026 · DOI

  • There is a need to understand the effect of awareness programs on the spread of diseases. The existing models do not consider the effect of awareness programs. The paper fills this gap by proposing a new mathematical model.

    Mathematical Modeling for the Spread and Control of Infectious Diseases by Spread of Awareness in Human Population · 2026 · DOI

  • Future research could explore the application of the model to specific diseases. Future research could investigate the effects of different types of time-dependent latency and spatial heterogeneity.

    Threshold dynamics of a reaction–diffusion epidemic model with an almost periodic time-dependent delay · 2026 · DOI

  • The paper identifies a gap in the existing literature on compartmental models, which assume individuals become contagious immediately upon infection. The paper also identifies a gap in the application of almost periodic functions to modeling seasonal variations.

    Threshold dynamics of a reaction–diffusion epidemic model with an almost periodic time-dependent delay · 2026 · DOI

  • The paper suggests analyzing the transient dynamics for matrices with higher rank. The paper suggests designing optimal control strategies for the NBF-SIR model.

    Network behavioral-feedback SIR epidemic model · 2026 · DOI

  • The classical SIR model relies on homogeneity assumptions that are often unrealistic. There is a need for a model that incorporates an endogenous behavioral response to the epidemic.

    Network behavioral-feedback SIR epidemic model · 2026 · DOI

  • By introducing the h-inner product, the positivity of numerical solutions is unconditionally guaranteed without mesh constraints, overcoming a key limitation of classical methods.

    An Improved Finite Element Method with Unconditional Positivity for a Reaction-diffusion HIV Infection Model with Spatial Heterogeneity · 2026 · DOI

  • Further study of the evolution of density-dependent dispersal strategies in competing species. Investigation of the effects of non-constant cross- and self-diffusion coefficients on the evolution of dispersal.

    En busca de una teoría racional de la tradición · 1983 · DOI

  • The lack of understanding of the role of population density-dependent dispersal in the evolution of dispersal. The need for a mathematical framework for studying this problem.

    En busca de una teoría racional de la tradición · 1983 · DOI

  • Future work may address these by developing formal analytical proofs for the bifurcation boundaries or extending the framework to incorporate environmental stochasticity and time delays to further explore the robustness of the observed oscillatory regimes. The analysis relies on numerical bifurcation methods and assumed parameter values for specific interaction rates, as explicit analytical Hopf conditions for the three-dimensional system remain to be derived.

    Dynamics of Predator-Prey Model with Holling Type II Involving Predator Stage-Structured and Cannibalism · 2026 · DOI

  • Lemma 5.3 establishes convergence of (uⁿ₁, uⁿ₂, uⁿ₃) to (Ẽ*, Ĩ*, R̃*) as l → ∞ for solutions in Γ+, but the rate of convergence and the uniform bounds on the convergence interval [l₀, ∞) are not specified. Quantifying this convergence rate would enable explicit bounds on the minimum l value needed to approximate the endemic state with prescribed accuracy in numerical simulations.

    On the dynamics of a diffusive SEIRS epidemic model · 2026 · DOI

  • The case where dS = dE = dI = dR (equal diffusion) receives special treatment in equation (6.13)-(6.14), but the paper does not characterize the minimum diffusion coefficient ratio min(dE/dS, dI/dS, dR/dS) required for EE solutions to exist when diffusion coefficients are unequal. This gap prevents precise determination of disease persistence in heterogeneous spatial environments.

    On the dynamics of a diffusive SEIRS epidemic model · 2026 · DOI

  • The paper does not provide explicit conditions on the magnitude of travel loss parameters (εS_ij, εI_ij) required to prevent strain invasion across patches or to guarantee exclusion of the less-competitive strain, leaving practical thresholds for disease control interventions unspecified.

    Effects of host migration and travel loss on strain competition in a two-patch SIR model · 2026 · DOI

  • The model structure assumes the same form of contact rates (β) and recovery rates (γ, α) for both strains within each patch; sensitivity analysis on how strain-specific differences in transmissibility and virulence affect the strain competition outcomes under migration is absent.

    Effects of host migration and travel loss on strain competition in a two-patch SIR model · 2026 · DOI

  • The complexity of the model and the optimal control strategy. The lack of data on the spread of racism. The difficulty in accounting for other factors that may influence the spread of racism.

    Modeling and Analysis of the Spread of Racism in the Community with Optimal Control Strategy · 2026 · DOI

  • To develop more complex models that account for other factors that may influence the spread of racism. To apply the optimal control strategy to other social issues, such as the spread of diseases or misinformation. To conduct further studies on the effectiveness of the optimal control strategy in different communities.

    Modeling and Analysis of the Spread of Racism in the Community with Optimal Control Strategy · 2026 · DOI

  • Future research can focus on applying the results to various fields, including engineering, physical sciences, and biological systems. Future research can aim to extend the partial (cross) monotone iteration method to more general systems.

    Existence of Traveling Waves of Lotka Volterra Type Models with Delayed Diffusion Term and Partial Quasimonotonicity · 2026 · DOI

  • The paper identifies a gap in the study of systems with delays. The paper aims to extend the partial (cross) monotone iteration method to systems satisfying a partial quasi-monotone condition.

    Existence of Traveling Waves of Lotka Volterra Type Models with Delayed Diffusion Term and Partial Quasimonotonicity · 2026 · DOI

  • The study identifies a gap in existing research on eco-epidemic models and bifurcation analysis. The study addresses the need for a more comprehensive understanding of the interplay between ecological dynamics and infectious diseases.

    Invasion Number in Fear and Refuge Driven Spatial Predator-Prey Model with Nonlinear Harvesting · 2026 · DOI

  • Future research can build on the paper's findings to develop more effective vaccination strategies. Future research can also explore the application of the paper's results to other diseases.

    On Multi-Group Chickenpox Mathematical Epidemic Models with Effective Vaccination and Re-Infection Challenges · 2026 · DOI

  • The paper identifies a gap in the understanding of multi-age group chickenpox epidemic models with effective vaccination. The paper aims to fill this gap by providing a stability analysis of the disease-free and endemic equilibrium points.

    On Multi-Group Chickenpox Mathematical Epidemic Models with Effective Vaccination and Re-Infection Challenges · 2026 · DOI

  • The presence of non-monotonic coupling under spatial heterogeneity complicates the analysis of steady states in the model. The model needs to account for the spatial dynamics of host resources. The model needs to evaluate the effectiveness of different control measures.

    Spatiotemporal evolution of a pine wilt disease model integrating infectious disease transmission and predator–prey interactions · 2026 · DOI

  • To extend the model to other regions and evaluate its effectiveness in different environments. To incorporate other factors that may affect the spread of pine wilt disease. To develop more effective management strategies for pine wilt disease.

    Spatiotemporal evolution of a pine wilt disease model integrating infectious disease transmission and predator–prey interactions · 2026 · DOI

  • Future research could focus on the development of more effective biological control strategies. The study of the impact of environmental factors on the propagation dynamics of yellows viruses could also be explored.

    Propagation dynamics of reaction-diffusion systems in sugar beet agro-ecosystems · 2026 · DOI

  • The study identifies a gap in the understanding of the propagation dynamics of yellows viruses in sugar beet agro-ecosystems. The paper aims to fill this gap by analyzing the spreading characteristics of infected hosts and infected vectors.

    Propagation dynamics of reaction-diffusion systems in sugar beet agro-ecosystems · 2026 · DOI

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81 open questions have been extracted from the limitations and future-work passages of 441 Mathematical and Theoretical Epidemiology and Ecology Models papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

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