SIR Model

πŸ“ˆ Temporal Lags and Vector Bionomics: The Time-Delay SIR Model 🦟

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──────────────────────────────────────────── 🧠 Conceptual Overview In mathematical epidemiology, the Time-Delay SIR model is a mechanistic framework designed specifically for vector-borne pathogens such as dengue virus. Unlike classical SIR models that assume instantaneous transitions between epidemiological states, this formulation explicitly incorporates biologically realistic waiting times using delay differential equations. Its central feature is the Extrinsic Incubation Period … Read more

πŸ“ˆ The Silent Reservoir: The Subclinical Infection SEIR Model for Dengue

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──────────────────────────────────────── 🧠 Conceptual OverviewIn arboviral epidemiology, the Subclinical Infection SEIR model provides a mechanistic framework for quantifying hidden drivers of dengue transmission. Unlike standard models that focus only on symptomatic infections, this formulation explicitly represents asymptomatic or subclinical infections, which often remain undetected yet contribute substantially to the viraemic pool and sustain mosquito infection. By … Read more

πŸ“ˆ Climatic Forcing: The SIR Model with Time-Varying Transmission Ξ²(t)

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──────────────────────────────────────── 🧠 CONCEPTUAL OVERVIEWIn mathematical epidemiology, the SIR model with time-varying transmission Ξ²(t) provides a foundational framework for studying climate-sensitive diseases such as dengue. Unlike classical autonomous SIR models, this non-autonomous formulation explicitly accounts for environmental modulation of transmission, particularly through temperature-driven changes in Aedes aegypti bionomics, including biting rates, survival, and the extrinsic incubation … Read more

🦟 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 (β€œhotspots”) 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

πŸ“ˆ 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

πŸ“ˆ 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:β€’ Imperfect mass vaccination with leaky efficacyβ€’ Temperature-dependent mosquito life-history traits, including biting, recruitment, mortality, and extrinsic incubationβ€’ Continuous virus importation via infected travelersβ€’ 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 contactβ€”such as clinical isolationβ€”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, β€œcontact 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: β€’ Biological saturation: Mosquito biting is limited by gonotrophic cycles and host availability.β€’ Behavioral feedback: As human case counts rise, communities adopt protective measures (e.g., repellents, screens, reduced outdoor activity), reducing … Read more

πŸ“ˆ 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