ODE

šŸŒ Beyond the Vector: The 10-Compartment Novel Malaria Model

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The Novel Malaria Mathematical Model is an expanded SEIR-based compartmental framework designed to capture malaria transmission through both classical mosquito-borne pathways and non-vector routes such as blood transfusion, congenital transmission, and human-to-human exposure in healthcare settings. By integrating vaccination, treatment, recovery, and multiple exposure mechanisms, this ten-compartment structure provides a comprehensive representation of malaria persistence … Read more

šŸŒ”ļø Modeling Environmental Drivers: The SIRā€“SI Framework for Vector-Borne Disease

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The Susceptibleā€“Infectedā€“Recovered model for humans coupled with a Susceptibleā€“Infected model for mosquitoes (SIRā€“SI) is a foundational compartmental framework in mathematical epidemiology for studying vector-borne infectious diseases such as malaria. The model explicitly captures the bidirectional transmission dynamics between human hosts and mosquito vectors. A key extension of this framework integrates environmental driversā€”most notably temperature and … Read more

šŸ¦Ÿ Beyond SIR: Advanced Rossā€“Macdonald Style Models

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Advanced Rossā€“Macdonald style models constitute the mathematical foundation for understanding and quantifying transmission dynamics of vector-borne diseases, most notably malaria and dengue. These models extend beyond simple SIR-type formulations by explicitly coupling vertebrate host dynamics with insect vector dynamics. Subsequent refinements introduced by later theoretical developments incorporated critical biological realism, including mosquito mortality during the … Read more

šŸ¦  Vector Control and Policy: The Rossā€“Macdonald Model with Quarantine

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The Rossā€“Macdonald Model with Quarantine (RM-Q) is a deterministic compartmental framework developed for vector-borne diseases, particularly malaria, that explicitly incorporates public health isolation strategies for infected humans. By introducing a quarantined human compartment, the model quantifies how reducing mosquitoā€“human contact through isolation policies alters transmission dynamics. This extension is especially relevant for elimination settings, where … Read more

šŸ¦Ÿ Dynamics with Memory: The Delayed Rossā€“Macdonald Model

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The Delayed Rossā€“Macdonald Model represents a major refinement of classical mechanistic models for vector-borne diseases such as malaria. Its defining innovation is the explicit incorporation of fixed pathogen incubation periods in both the human host and the insect vector. These intrinsic and extrinsic incubation periods are modeled as time delays rather than exponentially distributed transition … Read more

šŸ’‰ Epidemiological Planning: The SEIVRD Compartmental Model

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The Susceptibleā€“Exposedā€“Symptomaticā€“Vaccinatedā€“Recoveredā€“Deceased (SEIVRD) compartmental model is an enhanced deterministic framework developed to study epidemic dynamics in settings where latency, vaccination, and disease-induced mortality must be explicitly represented. By extending classical SEIR-type models to include vaccination and death as distinct epidemiological states, this framework supports strategic public health planning in contexts where vaccine deployment, immunity loss, … Read more

šŸ“Š Modeling Detection Errors: The SIQRD Framework for False Positives

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The Susceptibleā€“Infectiousā€“Quarantinedā€“Recoveredā€“Dead (SIQRD) model is a compartmental framework in mathematical epidemiology designed to analyze infectious disease dynamics under testing and isolation policies. A defining feature of this model is its explicit treatment of quarantine following detection, including the epidemiological and operational consequences of false-positive test results. By allowing quarantined but uninfected individuals to return to … Read more

šŸ§¬ SEAIRD Model: Dissecting Asymptomatic Spread and Mortality

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The Susceptibleā€“Exposedā€“Asymptomaticā€“Infectiousā€“Recoveredā€“Dead (SEAIRD) model is an advanced compartmental framework in mathematical epidemiology designed to capture the full spectrum of infection dynamics in viral diseases characterized by asymptomatic transmission and non-negligible mortality. By explicitly modeling both a latent incubation phase and a distinct asymptomatic infectious class, the SEAIRD model provides a refined representation of epidemic progression … Read more

šŸ’€ Tracking Outcomes: The SEIRD Compartmental Model

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The Susceptibleā€“Exposedā€“Infectiousā€“Recoveredā€“Dead (SEIRD) model is a deterministic compartmental framework widely used in mathematical epidemiology to analyze infectious disease dynamics while explicitly accounting for disease-induced mortality. By extending the classical SEIR structure to include a distinct death compartment, the SEIRD model enables direct quantification of epidemic severity and overall population impact. This feature is particularly important … Read more

šŸ“ˆ High-Granularity Control: Analyzing Disease Dynamics with the SICARQD Model

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The Susceptibleā€“Incubatingā€“Contagiousā€“Awareā€“Quarantinedā€“Recoveredā€“Deceased (SICARQD) model is an advanced compartmental framework developed to explicitly evaluate the epidemiological impact of public health interventions, particularly detection and quarantine policies. By distinguishing multiple infection stages and isolation processes, the model captures critical features of modern viral epidemics, such as pre-symptomatic transmission, delayed awareness, and compliance-driven isolation. This level of granularity … Read more