In this manuscript, we formulate a mathematical model of the deadly COVID-19 pandemic to understand the dynamic behavior of COVID-19. For the dynamic study, a new SEIAPHR fractional model was purposed in which infectious individuals were divided into three sub-compartments. The purpose is to construct a more reliable and realistic model for a complete mathematical and computational analysis and design of different control strategies for the proposed Caputo–Fabrizio fractional model. We prove the existence and uniqueness of solutions by employing well-known theorems of fractional calculus and functional analyses. The positivity and boundedness of the solutions are proved using the fractional-order properties of the Laplace transformation. The basic reproduction number for the model is computed using a next-generation technique to handle the future dynamics of the pandemic. The local–global stability of the model was also investigated at each equilibrium point. We propose basic fixed controls through manipulation of quarantine rates and formulate an optimal control problem to find the best controls (quarantine rates) employed on infected, asymptomatic, and “superspreader” humans, respectively, to restrict the spread of the disease. For the numerical solution of the fractional model, a computationally efficient Adams–Bashforth method is presented. A fractional-order optimal control problem and the associated optimality conditions of Pontryagin maximum principle are discussed in order to optimally reduce the number of infected, asymptomatic, and superspreader humans. The obtained numerical results are discussed and shown through graphs.

Historically, humans have been infected by mosquito-borne diseases, including dengue fever and malaria fever. There is an urgent need for comprehensive methods in the prevention, control, and awareness of the hazards posed by dengue and malaria fever to public health. We propose a new mathematical model for dengue and malaria co-infection with the aim of comprehending disease dynamics better and developing more efficient control strategies in light of the threat posed to public health by co-infection. The proposed mathematical model comprises four time-dependent vector population classes ($\mathcal{S}\mathcal{E}{\mathcal{I}}_d{\mathcal{I}}_m$) and seven host population classes ($\mathbb{S}\mathbb{E}{\mathbb{I}}_d{\mathbb{I}}_m{\mathbb{I}}_{dm}\mathbb{T}\mathbb{R}$). First, we show that the proposed model is well defined by proving that it is bounded and positive in a feasible region. We further identify the equilibrium states of the model, including disease-free and endemic equilibrium points, where we perform stability analysis at equilibrium points. Then, we determine the reproduction number $R_0$ to measure the level of disease containment. We perform a sensitivity analysis of the model’s parameters to identify the most critical ones for potential control strategies. We also prove that the proposed model is well posed. Finally, the article examines three distinct co-infection control measures, including spraying or killing vectors, taking precautions for one’s own safety, and reducing the infectious contact between the host and vector populations. The control analysis of the proposed model reveals that all control parameters are effective in disease control. However, self-precaution is the most effective and accessible method, and the reduction of the vector population through spraying is the second most effective strategy to implement. Disease eradication is attainable as the vector population decreases. The effectiveness of the implemented strategies is also illustrated with the help of graphs.

The COVID-19 pandemic has become a worldwide concern and has caused great frustration in the human community. Governments all over the world are struggling to combat the disease. In an effort to understand and address the situation, we conduct a thorough study of a COVID-19 model that provides insights into the dynamics of the disease. For this, we propose a new $L_S{H}_{S}EAIHR$ COVID-19 model, where susceptible populations are divided into two sub-classes: low-risk susceptible populations, $L_S$, and high-risk susceptible populations, $H_S$. The aim of the subdivision of susceptible populations is to construct a model that is more reliable and realistic for disease control. We first prove the existence of a unique solution to the purposed model with the help of fundamental theorems of functional analysis and show that the solution lies in an invariant region. We compute the basic reproduction number and describe constraints that ensure the local and global asymptotic stability at equilibrium points. A sensitivity analysis is also carried out to identify the model’s most influential parameters. Next, as a disease transmission control technique, a class of isolation is added to the intended $L_S{H}_{S}EAIHR$ model. We suggest simple fixed controls through the adjustment of quarantine rates as a first control technique. To reduce the spread of COVID-19 as well as to minimize the cost functional, we constitute an optimal control problem and develop necessary conditions using Pontryagin’s maximum principle. Finally, numerical simulations with and without controls are presented to demonstrate the efficiency and efficacy of the optimal control approach. The optimal control approach is also compared with an approach where the state model is solved numerically with different time-independent controls. The numerical results, which exhibit dynamical behavior of the COVID-19 system under the influence of various parameters, suggest that the implemented strategies, particularly the quarantine of infectious individuals, are effective in significantly reducing the number of infected individuals and achieving herd immunity.

In this manuscript, we present a novel mathematical model for understanding the dynamics of HIV/AIDS and analyzing optimal control strategies. To capture the disease dynamics, we propose a new Caputo-Fabrizio fractional-order mathematical model denoted as SE_IE_UPIATR, where the exposed class is subdivided into two categories: exposed-identified E_I and exposed-unidentified E_U individuals. Exposed-identified individuals become aware of the disease within three days, while exposed-unidentified individuals remain unaware for more than three days. Simultaneously, we introduce a treatment compartment with post-exposure prophylaxis (PEP), represented as P, designed for individuals of the exposed identified class. These individuals initiate treatment upon identification and continue for 28 days, resulting in full recovery from HIV. Additionally, we categorize infectious individuals into two groups: under-treatment individuals, denoted as T, and those with fully developed AIDS not receiving antiretroviral therapy (ART) treatment, denoted as A. We establish that the proposed model has a unique, bounded, and positive solution, along with other fundamental characteristics. Disease-free and endemic equilibrium points and their associated properties (such as the reproduction number R 0 and stability analysis) are determined. Sensitivity analysis is performed to assess the impact of parameters on R 0 and hence on the disease dynamics. Finally, we formulate a fractional optimal control problem to examine strategies for minimizing HIV/AIDS infection while keeping costs at a minimum. We adopt the use of condoms and changes in sexual habits as optimal controls. The numerical results are presented and discussed through graphs.

The co-infection of corona and influenza viruses has emerged as a significant threat to global public health due to their shared modes of transmission and overlapping clinical symptoms. This article presents a novel mathemati... | Find, read and cite all the research you need on Tech Science Press