We formulate a dynamic mathematical model that describes the interaction of immune system with human immunodeficiency virus (HIV) and permits drug "cocktail " therapies. derive HIV therapeutic strategies by formulating analyzing an optimal control problem using two types treatments representing reverse transcriptase (RT) in hibitors protease inhibitors (PIs). Continuous therapies are found solving corresponding optimality systems. In addition, ideas from programming, we suboptimal structured...

In this paper we study the dynamics of a vector-transmitted disease using two deterministic models. First, look at time dependent prevention and treatment efforts, where optimal control theory is applied. Using analytical numerical techniques, it shown that there are cost effective efforts for hosts host-vector contacts. Then, considered autonomous counter part mode established global stability results based on reproductive number. The model applied to effects controls malaria while keeping...

Since the 1980s, there has been a worldwide re-emergence of vector-borne diseases including Malaria, Dengue, Yellow fever or, more recently, chikungunya. These viruses are arthropod-borne (arboviruses) transmitted by arthropods like mosquitoes <em>Aedes</em> genus. The nature these arboviruses is complex since it conjugates human, environmental, biological and geographical factors. Recent researchs have suggested, in particular during Réunion Island epidemic 2006, that transmission <em>Aedes...

Countries around the world have taken control measures to mitigate spread of COVID-19, including Korea. Social distancing is considered an essential strategy reduce transmission in absence vaccination or treatment. While interventions been successful controlling COVID-19 Korea, maintaining current restrictions incurs great social costs. Thus, it important analyze impact different polices on epidemic. To model outbreak, we use extended age-structured SEIR with quarantine and isolation...

Abstract We consider optimal dynamic multidrug therapies for human immunodeficiency virus (HIV) type 1 infection. In this context, we describe an tracking problem attempting to drive the states of system a stationary state in which viral load is low and immune response strong. feedback control with full‐state as well partial‐state measurements. case measurement, estimator constructed based on T‐cell count demonstrate by numerical simulations that anticipation disease progression, strategy...

We consider the increasingly important and highly complex immunological control problem: of dynamics immunosuppression for organ transplant recipients. The goal in this problem is to maintain delicate balance between over-suppression (where opportunistic latent viruses threaten patient) under-suppression rejection transplanted probable). First, a mathematical model formulated describe immune response both viral infection introduction donor kidney renal recipient. Some numerical results are...

We consider a feedback control problem of susceptible-infective-recovered (SIR) model to design an efficient vaccination strategy for influenza outbreaks. formulate optimal that minimizes the number people who become infected, as well costs vaccination. A methodology based on Hamilton-Jacobi-Bellman (HJB) equation is introduced derive function. describe viscosity solution, which approximation solution HJB equation. successive method combined with upwind finite difference discussed find...

Abstract Background The reproduction number is one of the most crucial parameters in determining disease dynamics, providing a summary measure transmission potential. However, estimating this value particularly challenging owing to characteristics epidemic data, including non-reproducibility and incompleteness. Methods In study, we propose mathematical models with different population structures; each these can produce data on cases influenza A(H1N1)pdm09 South Korea. These structured...

Abstract The Trivers-Willard hypothesis (TWH) plays a central role in understanding the optimal investment strategies to male and female offspring. Empirical studies of TWH, however, yielded conflicting results. Here, we present models predict comprehensive multi-element parental composed primary sex ratio, brood size, resource allocation among offspring, resultant secondary ratio. Our results reveal that strategy depends on differences shape offspring fitness function rather than variance....

Abstract We investigate an optimal control problem of various epidemic models with uncertainty using stochastic differential equations, random and agent‐based models. discuss deep reinforcement learning (RL), which combines RL neural networks, as one method to solve the problem. The Q‐network algorithm is introduced approximate action‐value function consequently obtain policy. Numerical simulations show that in order effectively prevent spread infectious diseases, it essential vaccinate at...

In the paper considers a problem of stabilizing system differential equations with delay that described HIV infection dynamics mathematical model. A control is constructed basing on method explicit solutions Generalized Riccati Equations theory analytical constructing regulator for systems functional equations. For construct feedback we use second variant generalized First and third variants stabilization discussed in other authors articles. To determine parameters based equation should be...