ODE

📈 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 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

📈 Endemic Persistence: The SI Model with Demography 🧬

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──────────────────────────────────────────── 🧠 Conceptual Overview In mathematical biology, the SI model with demography is a foundational framework for studying infections that persist for life. In contrast to closed-population SI models—where infection eventually spreads to every individual—the inclusion of demographic processes (births and deaths) fundamentally alters long-term dynamics. Continuous recruitment introduces new susceptible individuals, while mortality removes … Read more

📈 The Stealth of Transmission: The SEPIR Model 🛡️

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──────────────────────────────────────────── 🧠 Conceptual Overview In advanced epidemiological surveillance, the SEPIR model represents a critical refinement of classical compartmental frameworks for infectious diseases. It is specifically designed to capture pre-symptomatic transmission, a mechanism by which infected individuals spread pathogens before the onset of clinical symptoms. Unlike standard SEIR models, which assume infectiousness begins only after symptoms … Read more