Mathematical Analysis of Two Strains Covid-19 Disease Using SEIR Model

The biggest public health problem facing the whole world today is the COVID-19 pandemic. From the time COVID-19 came into the limelight, people have been losing their loved ones and relatives as a direct result of this disease. Here, we present a six-compartment epidemiological model that is deterministic in nature for the emergence and spread of two strains of the COVID-19 disease in a given community, with quarantine and recovery due to treatment. Employing the stability theory of differential equations, the model was qualitatively analyzed. We derived the basic reproduction number  for both strains and investigated the sensitivity index of the parameters. In addition to this, we probed the global stability of the disease-free equilibrium. The disease-free equilibrium was revealed to be globally stable, provided and the model exhibited forward bifurcation. A numerical simulation was performed, and pertinent results are displayed graphically and discussed

Mathematical Analysis of Two Strains Covid-19 Disease Using SEIR Model

The biggest public health problem facing the whole world today is the COVID-19 pandemic. From the time COVID-19 came into the limelight, people have been losing their loved ones and relatives as a direct result of this disease. Here, we present a six-compartment epidemiological model that is deterministic in nature for the emergence and spread of two strains of the COVID-19 disease in a given community, with quarantine and recovery due to treatment. Employing the stability theory of differential equations, the model was qualitatively analyzed. We derived the basic reproduction number  for both strains and investigated the sensitivity index of the parameters. In addition to this, we probed the global stability of the disease-free equilibrium. The disease-free equilibrium was revealed to be globally stable, provided and the model exhibited forward bifurcation. A numerical simulation was performed, and pertinent results are displayed graphically and discussed

Optimal Control and Cost Effectiveness Analysis of SIRS Malaria Disease Model with Temperature Variability Factor

In this study, we proposed and analyzed the optimal control and cost-effectiveness strategies for malaria epidemics model with impact of temperature variability. Temperature variability strongly determines the transmission of malaria. Firstly, we proved that all solutions of the model are positive and bounded within a certain set with initial conditions. Using the next-generation matrix method, the basic reproductive number at the present malaria-free equilibrium point was computed. The local stability and global stability of the malaria-free equilibrium were depicted applying the Jacobian matrix and Lyapunov function respectively when the basic reproductive number is smaller than one. However, the positive endemic equilibrium occurs when the basic reproductive number is greater than unity. A sensitivity analysis of the parameters was conducted; the model showed forward and backward bifurcation. Secondly, using Pontryagin’s maximum principle, optimal control interventions for malaria disease reduction are described involving three control measures, namely use of insecticide-treated bed nets, treatment of infected humans using anti-malarial drugs, and indoor residual insecticide spraying. An analysis of cost-effectiveness was also conducted. Finally, based on the simulation of different control strategies, the combination of treatment of infected humans and insecticide spraying was proved to be the most efficient and least costly strategy to eradicate the disease

Monitoring microorganisms’ growth using multisensor electrochemical devices

Mestrado de dupla diplomação com a Université Libre de TunisSome microorganisms contribute beneficially in processing, safety and quality of certain food products. However, many microorganisms are involved in processes that cause undesirable effects on food, or on the health of consumers, leading to spoilage or to occurrence of foodborne diseases. For that, microbiological surveillance of food corresponds to an area of great interest to ensure the quality and the safety of food to prevent foodborne diseases. Indeed, for reasons related to sampling, methodology and distribution of the microorganisms in the matrix, microbiological analysis for itself does not guarantee the safety of a final product analyzed. For that, a possible promising alternative to the traditional diagnostic methods in the electronic sensors such as the E-tongues that has been used for different applications in food and pharmaceutical industries, they have been useful for the detection of bacterial contamination or diagnosis of infections. The aim of the present study was the detection and discrimination of microorganism that played an important role in food and environmental areas, namely E. coli, Enterococcus faecalis, Pseudomonas aeruginosa and S. aureus. In this context, electronic tongues (E-tongues) have been employed for the detection and screening of microorganisms. Thus; the use of a potentiometric E-tongue, comprising lipid polymeric sensor membranes, together with unsupervised and supervised chemometric tools (e.g., principal component analysis, PCA; linear discriminant analysis, LDA; and. multiple linear regression models, MLRM) was evaluated aiming to explore the advantages of these innovative (bio)sensing devices for microorganism’s recognition and discrimination, in aqueous solutions. Our results showed that the potentiometric signals profiles acquired by the 40 E-tongue sensors allowed a satisfactory unsupervised recognition of P. aeruginosa and E. faecalis, contrary to E. coli and S. aureus, showed a clear over-plotting. Still to further assess the E-tongue classification capability, a LDA was performed since it represents the most discriminant and non-redundant sensors selected by the SA algorithm. The supervised discriminant model allowed to classify 100% of the original grouped data. Overall, the unsupervised and supervised classification performances clearly showed the potential use of the E-tongue as an accurate and fast recognition device of the four microorganisms studied.Alguns microrganismos contribuem para a segurança e qualidade de certos produtos alimentares. No entanto, outros grupos de microrganismos causam efeitos indesejáveis nos alimentos provocando a sua deterioração ou inclusive dando origem a doenças de origem alimentar colocando em risco a saúde dos consumidores. Neste contexto, a vigilância microbiológica dos alimentos é uma área de grande relevância de forma a garantir a qualidade e a segurança dos alimentos. Contudo, as técnicas analíticas convencionais utilizadas na deteção de microrganismos em alimentos são caras e demoradas. Alternativamente, podem ser aplicadas outras técnicas, nomeadamente línguas eletrónicas (LE), para cumprir essa tarefa crítica. Com este estudo pretendeu-se estudar a capacidade de deteção e discriminação de microrganismos que desempenham um papel importante nas áreas alimentares e ambientais, nomeadamente Escherichia coli, Enterococcus faecalis, Pseudomonas aeruginosa e Staphylococcus aureus. Para tal, utilizou-se uma LE potenciométrica e o seu desempenho de deteção foi avaliado recorrendo a ferramentas quimiométricas não supervisionadas e supervisionadas (análise principal de componentes, ACP; análise discriminante linear ADL). Os resultados mostraram que os sinais potenciométricos adquiridos pelos sensores da LE permitem reconhecer satisfatoriamente e não supervisionado a P. aeruginosa e o E. faecalis, ao contrário da E. coli e S. aureus A capacidade de classificação da LE foi ainda avaliada pela ADL, com vista a identificar os sensores não redundantes e com maior potencial discriminante. O modelo discriminatório supervisionado permitiu classificar 100% dos dados originais. Globalmente, os desempenhos de classificação confirmaram a possível utilização da LE como um dispositivo de reconhecimento preciso e rápido dos quatro microrganismos estudados