Mathematical Analysis of the Ross-Macdonald Model with Quarantine

Ronald Ross: Pioneer of Malaria Research and Nobel Laureate

Sir Ronald Ross, a British medical doctor and researcher, is renowned for his pioneering work in malaria research. His discovery of the malaria parasite's lifecycle within mosquitoes revolutionized the understanding and control of malaria, transitioning the field from the miasma theory to vector-based strategies. This literature review aims to explore the comprehensive contributions of Ronald Ross to malaria research and their enduring impact on public health.

Time lag effect on malaria transmission dynamics in an Amazonian Colombian municipality and importance for early warning systems

Malaria remains a significant public health problem worldwide, particularly in low-income regions with limited access to healthcare. Despite the use of antimalarial drugs, transmission remains an issue in Colombia, especially among indigenous populations in remote areas. In this study, we used an SIR Ross MacDonald model that considered land use change, temperature, and precipitation to analyze eco epidemiological parameters and the impact of time lags on malaria transmission in La Pedrera-Amazonas municipality. We found changes in land use between 2007 and 2020, with increases in forested areas, urban infrastructure and water edges resulting in a constant increase in mosquito carrying capacity. Temperature and precipitation variables exhibited a fluctuating pattern that corresponded to rainy and dry seasons, respectively and a marked influence of the El Niño climatic phenomenon. Our findings suggest that elevated precipitation and temperature increase malaria infection risk in the following 2 months. The risk is influenced by the secondary vegetation and urban infrastructure near primary forest formation or water body edges. These results may help public health officials and policymakers develop effective malaria control strategies by monitoring precipitation, temperature, and land use variables to flag high-risk areas and critical periods, considering the time lag effect.

Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate

A four-dimensional delay differential equations (DDEs) model of malaria with standard incidence rate is proposed. By utilizing the limiting system of the model and Lyapunov direct method, the global stability of equilibria of the model is obtained with respect to the basic reproduction number R ₀. Specifically, it shows that the disease-free equilibrium E ⁰ is globally asymptotically stable (GAS) for R ₀ < 1, and globally attractive (GA) for R ₀ = 1, while the endemic equilibrium E* is GAS and E ⁰ is unstable for R ₀ > 1. Especially, to obtain the global stability of the equilibrium E* for R ₀ > 1, the weak persistence of the model is proved by some analysis techniques.

Modeling malaria transmission in Nepal: impact of imported cases through cross-border mobility

The cross-border mobility of malaria cases poses an obstacle to malaria elimination programmes in many countries, including Nepal. Here, we develop a novel mathematical model to study how the imported malaria cases through the Nepal-India open-border affect the Nepal government's goal of eliminating malaria by 2026. Mathematical analyses and numerical simulations of our model, validated by malaria case data from Nepal, indicate that eliminating malaria from Nepal is possible if strategies promoting the absence of cross-border mobility, complete protection of transmission abroad, or strict border screening and isolation are implemented. For each strategy, we establish the conditions for the elimination of malaria. We further use our model to identify the control strategies that can help maintain a low endemic level. Our results show that the ideal control strategies should be designed according to the average mosquito biting rates that may depend on the location and season.

The emergence of Dirofilaria repens in a non-endemic area influenced by climate change: dynamics of transmission using a mathematical model

Dirofilaria repens is a nematode affecting domestic and wild canids, transmitted by several species of mosquitoes of different genera. It usually causes a non-pathogenic subcutaneous infection in dogs and is the principal agent of human dirofilariasis in the Old World. The geographic distribution of D. repens is changing rapidly, and several factors contribute to the spread of the infection to non-endemic areas. A mathematical model for transmission of Dirofilaria spp. was built, using a system of ordinary differential equations that consider the interactions between reservoirs, vectors, and humans. The transmission simulations of D. repens were carried out considering a projection in time, with intervals of 15 and 100 years. For the dynamics of the vector, seasonal variations were presented as series with quarter periodicity during the year. The results of the simulations highlight the peak of contagions in the reservoir and in humans, a product of the action of the vector when it remains active throughout the year. A 300% infection increase in the reservoir was observed during the first decade and remains present in the population with a representative number of cases. When the vector maintains its density and infectivity during the year, the incidence of the infection in humans increases. Accumulated cases amount to 45 per 100,000 inhabitants, which corresponds to a cumulative incidence of 0.05%, in 85 years. This indicates that early prevention of infection in canids would significantly reduce the disease, also reducing the number of accumulated cases of human dirofilariasis by D. repens. The interaction between the simulations generated by the model highlights the sensitivity of the epidemiological curve to the periodicity of seasonality, reaffirming the hypothesis of the probability of movement of the zoonotic disease to non-endemic areas, due to climate change.