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Modeling the impact of temperature on the dynamics of carrier-dependent infectious diseases with control strategies
(American Institute of Mathematical Sciences, 2025) Shubham Chaudhry; Gauri Agrawal; Maia Martcheva; Arvind Kumar Misra
The spread of diseases poses significant threats to human health globally. The dynamic nature of infectious diseases, especially those that also rely on carriers (e.g., house flies) for transmission, requires innovative strategies to control their spread, as environmental conditions such as temperature, humidity, etc., affect the rate of growth of the carrier population. This study introduces a mathematical model to assess the effect of increasing global average temperature rise caused by carbon dioxide emissions and chemical control strategies on the dynamics of such diseases. The stability properties of feasible equilibrium solutions were discussed. Sensitivity analysis was also performed to highlight the key parameters that may help to design effective intervention strategies to control disease transmission. The model was further analyzed for an optimal control problem by incorporating a control measure on the application rate of chemical insecticides to reduce the carrier population. Through the combination of analytical techniques and numerical simulations, we have evaluated the effectiveness of chemical control strategies under varying epidemiological parameters. The model also explored the critical thresholds necessary for achieving disease control and eradication. Our results are valuable to public health officials and policymakers in designing effective interventions against carrier-dependent infectious diseases. © 2025 the Author(s), licensee AIMS Press.
Modeling the impact of air and water pollutants emitted from industries on rainfall
(World Scientific, 2025) Gauri Agrawal; Alok Kumar Agrawal; Arvind Kumar Misra
Rainfall regulates the hydrological cycle on the planet Earth, sustains our ecological system, and provides fresh water to all living beings. In the recent past, a deterioration in rainfall has been observed due to the increased level of pollutants emitted by industries in the environment. The presence of these industrial pollutants in the environment affects the processes of evaporation, condensation, and nucleation, requisite in forming cloud droplets and raindrops. In formulating the model, we categorize the total emissions of industrial pollutants into surface water pollutants and atmospheric pollutants in the environment to assess their effect explicitly on rainfall. We presume the natural formation rate of cloud droplets as a decreasing function of surface water pollutants. It is further assumed that the density of cloud droplets decreases due to atmospheric pollutants; and the surface water pollutants in regional water bodies increase due to the leaching of atmospheric pollutants during rainfall. To analyze the formulated model system, we use the qualitative theory of differential equations. The equilibrium solution is obtained, and its stability properties are discussed. The numerical analysis is performed to substantiate the analytically obtained results of the formulated mathematical model. The obtained results clearly show that industrial pollutants emitted into the environment exert a negative impact on rainfall. © 2025 World Scientific Publishing Company.

2025

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