Modelling and optimal control of multi strain epidemics, with application to COVID-19.

Reinfection and multiple viral strains are among the latest challenges in the current COVID-19 pandemic. In contrast, epidemic models often consider a single strain and perennial immunity. To bridge this gap, we present a new epidemic model that simultaneously considers multiple viral strains and reinfection due to waning immunity. The model is general, applies to any viral disease and includes an optimal control formulation to seek a trade-off between the societal and economic costs of mitigation. We validate the model, with and without mitigation, in the light of the COVID-19 epidemic in England and in the state of Amazonas, Brazil. The model can derive optimal mitigation strategies for any number of viral strains, whilst also evaluating the effect of distinct mitigation costs on the infection levels. The results show that relaxations in the mitigation measures cause a rapid increase in the number of cases, and therefore demand more restrictive measures in the future.

Numerical modeling of mosquito population dynamics of Aedes aegypti.

BACKGROUND: The global incidences of dengue virus have increased the interest in studying and understanding the mosquito population dynamics. It is predominantly spread by Aedes aegypti in the tropical and sub-tropical countries in the world. Understanding these dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. For this reason, a new model has been proposed to investigate the population dynamics of mosquitoes in a city. METHODS: The present paper discusses the numerical modeling of population dynamics of Ae. aegypti mosquitoes in an urban neighborhood of a city using the finite volume method. The model describes how populations spread through the city assisted by the wind. This model allows incorporating external factors (wind and chemical insecticides) and topography data (streets, building blocks, parks, forests and beach). The proposed model has been successfully tested in examples involving two Brazilian cities (City center, Juiz de Fora and Copacabana Beach, Rio de Janeiro). RESULTS: Invasion phenomena of Ae. aegypti mosquitoes have been observed in each of the simulations. It was observed that, inside the blocks, the growth of the population for both winged and aquatic phase causes an infestation of Ae. aegypti in a short time. Within the blocks the mosquito population was concentrated and diffused slowly. In the streets, there was a long-distance spread, which was influenced by wind and diffusion with a low concentration of mosquito population. The model was also tested taking into account chemical insecticides spread in two different configurations. It has been observed that the insecticides have a significant effect on the mosquito population for both winged and aquatic phases when the chemical insecticides spread more uniformly along all the streets in a neighborhood of a city. CONCLUSIONS: The presented methodology can be employed to evaluate and to understand the epidemic risks in a specific region of the city. Moreover the model allows an increase in efficiency of the existing mosquito population control techniques and to theoretically test new methods before involving the human population.