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.
This paper introduces a mathematical model which describes the dynamics of the spread of HIV in the human body. This model is comprised of a system of ordinary differential equations that involve susceptible cells, infected cells, HIV, immune cells and immune active cells. The distinguishing feature in the proposed model with respect to other models in the literature is that it takes into account cells that represent two distinct mechanisms of the immune system in the defense against HIV: the non-HIV-activated cells and the HIV-activated cells. With a view at minimizing the side effects of a treatment that employs a drug combination designed to attack the HIV at various stages of its life cycle, we introduce control variables that represent the infected patient's medication. The optimal control rule that prescribes the medication for a given time period is obtained by means of Pontryagin's Maximum Principle.
This article concerns the rigorous global analysis of a class of models introduced by Nowak and Bangham that describes in a fairly successful way the initial phases of the HIV dynamics in the human body as well as some generalizations that take into account mutation. We show that the biologically meaningful positive solutions to such models are all bounded and do not display periodic orbits. For the mutationless cases we characterize the dynamics in terms of certain dimensionless quantities, the so-called basic reproductive rate and the basic defense rate, and perform the stability analysis of the stationary solutions. As a consequence of our results, we conclude that the finite dimensional models under consideration cannot account, without further modifications, for the third phase of the HIV infection. We conclude by suggesting a modification that according to our numerical simulations may describe the collapse of the infected patient.
In this work we analyze the capacity of the human body to combat HIV. The model here treated takes into consideration four types of defense of an organism infected by HIV: susceptible defense cells, the infected immune cells, killer T cells, and the HIV specific killer T cells. This model therefore analyzes the interactions between the responses of killer T cells and HIV infections, evidencing how the immune system is attacked and how it defends. An optimal control problem is proposed to derive an optimal sequence of dosages in the standard drug treatment, in such a way as to minimize the side effects.
RESUMOEstudamos um modelo matemático que descreve a dinâmica de propagação do HIV no organismo humano. Este modeloé apresentado por meio de um sistema de equações diferenciais ordinárias que envolvem células suscetíveis, células infectadas, HIV, células de defesa e células de defesa ativas. A diferença desse modelo para outros encontrados na literatura são exatamente dois momentos de atuação do sistema imunológico na defesa contra o HIV: as células sem ativação para o HIV e as células ativadas para o HIV.O vírus da Imunodeficiência Humana, também conhecido como HIV, (sigla em inglês para human immunodeficiency virus),é da família dos retrovírus e o responsável pela AIDS. A infecção pelo HIV resulta em uma doença crônica e progressiva, que pode levarà destruição do sistema imunológico. A evolução da doença se caracteriza por uma elevada taxa de replicação viral, que resulta na emergência de variantes virais mais virulentas. A infecção pelo HIVé, atualmente, delineada pela contagem do número de células CD4+ pela quantidade de partículas virais no sangue (carga viral) e pelos sintomas clínicos.Para se reproduzir, o HIV une-seà membrana de uma célula vital para o sistema imunológico, a T4. O vírus libera seu RNA e uma enzima, a transcriptase reversa, com a qual fabrica o DNA viral. O DNA viral entra no núcleo e une-se ao DNA da célula, assumindo o comando. O resultado dessa uniãó e o DNA Pró-Viral que fabrica o RNA mensageiro com o código genético do vírus. O RNA mensageiro desloca-se para o citoplasma e produz os Vírions. Os Vírions saem da célula hospedeira como novos HIV's. Umúnico vírus gera muitos outros pontos para infectarem outras células (Amendoeira, 2009).O modelo proposto apresenta-se com a introdução de uma nova variável queé chamada de células específicas de defesa ativada. Consideramos que issoé extremamente importante para o modelo uma vez que em nosso organismo já possuímos células de defesa estando contaminado ou não. Faz parte do conjunto de células de qualquer indivíduo, possuir células suscetíveis e células de defesa que estão prontas para nos defender desde uma simples infecção até algo mais grave. Com a contaminação pelo HIV, o que ocorreé justamente a destruição dessas células que ficam impedidas de nos defender de uma simples gripe podendo tornar-se algo muito mais perigoso ao nosso organismo. Sendo assim, uma vez contaminada, a pessoa passa a ter também, células infectadas, vírus e células especificas de defesa ativada que estarão ali presentes com o intuito de tentar destruir exatamente o HIV.Neste trabalho, estamos propondo um novo modelo matemático para estudar a dinâmica do HIV no sistema imunológico humano. Estamos propondo modificações de vários modelos existentes na litera- * bolsista de Iniciação Científica PIBIC/CNPq
This work presents an ODE model for COVID-19 named SINDROME that incorporates quarantine, contagion dynamics, and environmentally mediated transmission based on the compartments. The SINDROME model introduces a new parameter that allows environmentally mediated transmission, moving quarantined individuals to the infected compartment. We developed a gray box model with the SINDROME, and fit over 169 worldwide regions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.