ODE

🦟 Targeting the Hotspots: A Structured Host–Vector Model for Dengue Superspreading

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──────────────────────────────────────── 🧠 CONCEPTUAL OVERVIEWClassical SIR models assume homogeneous mixing, which fails to capture the focal nature of dengue transmission. Empirical evidence indicates that a small fraction of locations or human subpopulations (“hotspots”) can drive a large fraction of transmission through elevated human–mosquito contact. This framework integrates (i) structured heterogeneity, (ii) temperature-dependent vector bionomics, and (iii) … Read more

📈 The Mosaic of Immunity: The SIR Model with Partial Immunity for Dengue

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──────────────────────────────────────── 🧠 CONCEPTUAL OVERVIEWDengue virus exists as four antigenically distinct serotypes (DENV-1 to DENV-4). Infection with one serotype confers lifelong homotypic immunity but only temporary cross-protection against heterologous serotypes. After cross-immunity wanes (typically within 6–18 months), individuals become susceptible to secondary infection, often with increased risk of severe disease due to antibody-dependent enhancement (ADE). This … Read more

📈 Immunological Barriers: The Temperature-Dependent Vector–Host Model with Imperfect Vaccination for Dengue

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──────────────────────────────────────── 🧠 CONCEPTUAL OVERVIEWDengue virus transmission is shaped by complex interactions among human immunity, vector ecology, and climate. This revised model integrates:• Imperfect mass vaccination with leaky efficacy• Temperature-dependent mosquito life-history traits, including biting, recruitment, mortality, and extrinsic incubation• Continuous virus importation via infected travelers• Explicit vector latency to represent EIP dynamics The framework enables … Read more

🦟 Breaking the Cycle: The SIR with Isolation Model for Dengue

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──────────────────────────────────────── 🧠 CONCEPTUAL OVERVIEWIn modeling vector-borne diseases like dengue, public health interventions that reduce human–mosquito contact—such as clinical isolation—can significantly disrupt transmission. The SIR with Isolation model extends the classic host–vector framework to explicitly represent the removal of viraemic individuals from the mosquito biting pool. This enables quantitative assessment of how rapid case isolation can … Read more

🦟 SIR–SEI Vector–Host Model with Contact Tracing for Dengue

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Precision Interruption Under Thermal Forcing and Virus Importation ──────────────────────────────────────── 🧠 CONCEPTUAL OVERVIEWThis model evaluates dengue transmission dynamics in settings where imported cases seed local outbreaks, and public health surveillance triggers focal vector control upon case detection. Unlike directly transmitted diseases, “contact tracing” in dengue does not interrupt human-to-human spread (which does not occur). Instead, it … Read more

🦟 SIR–SEI Vector–Host Model with Behavioral Saturation and Seasonal Forcing for Dengue

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Accounting for Biting Limits, Human Protective Responses, and Thermal Dynamics ──────────────────────────────────────── 🧠 CONCEPTUAL OVERVIEW This model captures dengue transmission under two key real-world constraints: • Biological saturation: Mosquito biting is limited by gonotrophic cycles and host availability.• Behavioral feedback: As human case counts rise, communities adopt protective measures (e.g., repellents, screens, reduced outdoor activity), reducing … Read more

🦟SIR–SEI Vector–Host Model with Symmetric Behavioral Feedback for Dengue

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Modeling Climate-Driven Transmission and Risk-Aware Human Responses ──────────────────────────────────────── 🧠 Conceptual Overview This model represents dengue transmission as a coupled host–vector process shaped by two interacting drivers: • Environmental forcing: Temperature regulates mosquito biting frequency, survival, and viral development.• Human behavioral adaptation: As infections rise, individuals and communities adopt protective actions (e.g., repellents, reduced outdoor exposure, … Read more

📈 Endemic Recurrence: The SIS Model with Demography and Seasonal Forcing

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──────────────────────────────────────────── 🧠 Conceptual OverviewIn infectious disease dynamics, the SIS (Susceptible–Infectious–Susceptible) model with demography provides a foundational framework for pathogens that do not confer immunity after recovery. Individuals who recover immediately return to the susceptible class, enabling repeated infections over their lifetime. By incorporating vital dynamics—specifically, births and natural deaths at equal per-capita rates—the model transitions … Read more

📈 The Dynamics of Endemicity: The SIR Model with Births and Deaths 🧬

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──────────────────────────────────────────── 🧠 Conceptual Overview In mathematical epidemiology, the SIR model with births and deaths, also known as the SIR model with demography or vital dynamics model, is the foundational framework for analyzing long-term disease persistence. Unlike closed-population SIR models that inevitably lead to pathogen extinction, this formulation introduces continuous population turnover. The permanent influx of … Read more

📈 The Indirect Link: The SIRE Environmental Model 🧪

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──────────────────────────────────────────── 🧠 Conceptual Overview In infectious disease modeling, the SIRE environmental model represents a major advance beyond purely person-to-person transmission frameworks. This model explicitly incorporates an Environmental Reservoir (E) to represent pathogens that persist outside the host in water, soil, or on contaminated surfaces. By introducing this indirect transmission pathway, the SIRE model captures scenarios … Read more