The SARS-CoV-2 epidemic posed devastating effects on public health, and there is growing concern about the proliferation of misinformation and the role awareness plays in altering the dynamics of an epidemic. We formulate an SEIR-type model of SARS-CoV-2 with three susceptible compartments, consisting of individuals who are unaware, aware and misinformed. The media-dependent reproduction number of our model is computed, and the global stability of the disease-free equilibrium and the uniform persistence of SARS-CoV-2 are established. Unknown parameter values of our model are estimated, using data on the cumulative number of cases of symptomatic infectious humans. Numerical simulations suggest a decrease in prevalence when susceptible humans transition from misinformed to aware humans, and when aware susceptible humans send media-related messages on the spread and control of SARS-CoV-2. Furthermore, there is an increase in the media-dependent reproduction number with an increase in misinformation. Finally, an optimal control of awareness and misinformation problem is formulated and analyzed. The optimal control results suggest that awareness and adherence to control measures, as well as the enhancement of media intensity, are vital in reducing disease prevalence within the population.These results highlight the role of awareness and misinformation in disease dynamics.

In this study, we develop and analyze a mathematical model to investigate the effects of treatment, vaccination, and sterile male mosquito release on malaria transmission. The model incorporates different levels of immunity, distinguishing between non-immune and semi-immune populations to better capture the dynamics of malaria spread and control. Using the next-generation matrix method, we compute the control reproduction number and establish the local asymptotic stability of the disease-free equilibrium when $\mathcal{R}_C<1$. A global sensitivity analysis with the reproduction number as the outcome variable is conducted to determine key parameters influencing malaria transmission. Additionally, we formulate and analyze an optimal control problem incorporating vaccination, treatment, and sterile male mosquito release as controls, and carry out a cost-effectiveness analysis to assess the economic feasibility of various intervention strategies. Our results suggest that a comprehensive intervention strategy that integrates treatment, vaccination, and sterile mosquito release is the most effective approach for reducing malaria transmission. However, from a cost-effectiveness perspective, prioritizing vaccination and treatment is the most feasible option in resource-limited settings.

Based on the immuno-epidemiological model concept, we propose a susceptible-infected-vaccinated-recovered epidemic model with between-host transmission and within-host infection, where disease transmission between hosts is described by a standard incidence rate and the within-host infection process is governed by a bilinear incidence rate. The basic reproduction number R-0(psi) in the between-host model strongly depends on the within-host infection process. If R-0(psi)<1, the disease-free steady state epsilon(0) of the between-host epidemic model is locally stable, and if R-0(psi)>1, the endemic steady state epsilon* of the between-host epidemic model is locally stable. If R-0(0)<1, the disease-free steady state epsilon(0) of the between-host epidemic model is globally stable. Furthermore, to better understand the roles of within-host treatment and between-host control in disease transmission, we formulated and studied an optimal control problem for the immuno-epidemiological model involving treatment and vaccination. Numerical simulations were conducted to demonstrate the effectiveness of the control strategies in various infection processes. The results showed that the duration of within-host treatment must be longer than the duration of vaccination to better control the spread of the disease.

In this study, we apply optimal control theory to an immuno-epidemiological model of HIV and opioid epidemics. For the multi-scale model, we used four controls: treating the opioid use, reducing HIV risk behaviour among opioid users, entry inhibiting antiviral therapy, and antiviral therapy which blocks the viral production. Two population-level controls are combined with two within-host-level controls. We prove the existence and uniqueness of an optimal control quadruple. Comparing the two population-level controls, we find that reducing the HIV risk of opioid users has a stronger impact on the population who is both HIV-infected and opioid-dependent than treating the opioid disorder. The within-host-level antiviral treatment has an effect not only on the co-affected population but also on the HIV-only infected population. Our findings suggest that the most effective strategy for managing the HIV and opioid epidemics is combining all controls at both within-host and between-host scales.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) that emerged in December 2019 poses an enormous threat in public health worldwide. The role of media coverage in disease outbreaks is crucial. Thus, we formulate an SEIR-type model of SARS-CoV-2 with two susceptible classes comprising individuals who are unconscious to SARS-CoV-2 spread and control and those who are conscious to SARS-CoV-2 spread and control due to media coverage. The disease-free equilibrium of our model is derived, and the media-dependent reproduction number ( ℛ_M ) is computed. We established the existence of a unique endemic equilibrium when ℛ_M>1 , and investigated the local and global stability of the disease-free equilibrium when ℛ_M<1 . The Latin Hypercube Sampling technique is used to identify parameters that are sensitive in reducing the media-dependent reproduction number. Using data on the cumulative number of cases of symptomatic infections from the state of Georgia, we estimated unknown parameters of our model. Numerical simulations of our model suggest that an increase in the messaging rate of COVID-related information by conscious susceptible humans suggest a decrease in the media-dependent reproduction number and the number of cumulative cases of symptomatic infectious humans. Also, an increase in waning awareness of COVID-related information results in an increase in prevalence. These results highlight the importance of media in the transmission and control of SARS-CoV-2 in the population.

COVID-19 is a respiratory disease caused by a recently discovered, novel coronavirus, SARS-COV2.The disease has led to over 81 million confirmed cases of COVID-19, with close to 2 million deaths.In the current social climate, the risk of COVID-19 infection is driven by individual and public perception of risk and sentiments.A number of factors influences public perception, including an individual's belief system, prior knowledge about a disease and information about a disease.In this paper, we develop a model for COVID-19 using a system of ordinary differential equations following the natural history of the infection.The model uniquely incorporates social behavioral aspects such as quarantine and quarantine violation.The model is further driven by people's sentiments (positive and negative) which accounts for the influence of disinformation.People's sentiments were obtained by parsing through and analyzing COVID-19 related tweets from Twitter, a social media platform across six countries.Our results show that our model incorporating public sentiments is able to capture the trend in the trajectory of the epidemic curve of the reported cases.Furthermore, our results show that positive public sentiments reduce disease burden in the community.Our results also show that quarantine violation and early discharge of the infected population amplifies the disease burden on the community.Hence, it is important to account for public sentiment and individual social behavior in epidemic models developed to study diseases like COVID-19.

COVID-19 is a respiratory disease caused by a recently discovered, novel coronavirus, SARS-COV-2. The disease has led to over 81 million confirmed cases of COVID-19, with close to two million deaths. In the current social climate, the risk of COVID-19 infection is driven by individual and public perception of risk and sentiments. A number of factors influences public perception, including an individual’s belief system, prior knowledge about a disease and information about a disease. In this article, we develop a model for COVID-19 using a system of ordinary differential equations following the natural history of the infection. The model uniquely incorporates social behavioral aspects such as quarantine and quarantine violation. The model is further driven by people’s sentiments (positive and negative) which accounts for the influence of disinformation. People’s sentiments were obtained by parsing through and analyzing COVID-19 related tweets from Twitter, a social media platform across six countries. Our results show that our model incorporating public sentiments is able to capture the trend in the trajectory of the epidemic curve of the reported cases. Furthermore, our results show that positive public sentiments reduce disease burden in the community. Our results also show that quarantine violation and early discharge of the infected population amplifies the disease burden on the community. Hence, it is important to account for public sentiment and individual social behavior in epidemic models developed to study diseases like COVID-19.

In this study, a novel mathematical model is developed to investigate the effectiveness of imperfect human vaccination against malaria. The model is a system of ordinary differential equations (ODEs) coupled with a first-order partial differential equation (PDE) that describes transmission of malaria with time-since-vaccination structure for vaccinated humans. The existence and uniqueness of the solution to the system are established, the basic reproduction number (R0) is calculated, and model stability analysis of equilibria is performed. The optimal control problem, subject to the model system, is formulated with the optimal vaccination rate that minimizes the cost of implementing the imperfect vaccination as well as the number of infected humans. The optimality system is solved numerically, and several optimal control scenarios which effectively control the disease are presented.

The Far North Region of Cameroon, a high risk cholera endemic region, has been experiencing serious and recurrent cholera outbreaks in recent years. Cholera outbreaks in this region are associated with cultural practices (traditional and religious beliefs). In this paper, we introduce a mathematical model of the influence of cultural practices on the dynamics of cholera in the Far North Region. Our model is an SEIR type model with a pathogen class and multiple susceptible classes based on traditional and religious beliefs. Using daily reported cholera cases from three health districts (Kaélé, Kar Hay and Moutourwa) in the Far North Region from June 25, 2019 to August 16, 2019, we estimate parameter values of our model and use Akaike information criterion (AIC) to demonstrate that our model gives a good fit for our data on cholera cases. We use sensitivity analysis to study the impact of each model parameter on the threshold parameter (control reproduction number), Rc, and the number of model predicted cholera cases. Finally, we investigate the effect of cultural practices on the number of cholera cases in the region.

A multi-strain within-host model of HIV with age structure, which explicitly incorporates the loss of free viral particles due to absorption into target cells upon infection, and shedding into the environment is formulated and analyzed. In our model, a time delay between viral entry into a target cell and viral replication is incorporated, and multiple virus strains compete for a population of target cells. Control is incorporated into the model via strain-specific reverse transcriptase and protease inhibitors. An optimal control problem subject to multiple drug treatments is formulated and analyzed. Existence, characterization and uniqueness of optimal control is established. Using the forward-backward sweep numerical method, numerical simulations are presented. Simulations suggest that a combination of reverse transcriptase and protease inhibitors for each strain of the infected cells and free viruses results in a delay in initial peak in the populations of infected cells and free viruses, the absence of relapse phase within the entire time horizon of control, and a decrease in the number of infected cells and free viruses.

Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward–backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.

We propose a new mathematical model studying control strategies of malaria transmission. The control is a combination of human and transmission-blocking vaccines and vector control (larvacide). When the disease induced death rate is large enough, we show the existence of a backward bifurcation analytically if vaccination control is not used, and numerically if vaccination is used. The basic reproduction number is a decreasing function of the vaccination controls as well as the vector control parameters, which means that any effort on these controls will reduce the burden of the disease. Numerical simulation suggests that the combination of the vaccinations and vector control may help to eradicate the disease. We investigate optimal strategies using the vaccinations and vector controls to gain qualitative understanding on how the combinations of these controls should be used to reduce disease prevalence in malaria endemic setting. Our results show that the combination of the two vaccination controls integrated with vector control has the highest impact on reducing the number of infected humans and mosquitoes.

We propose and study a mathematical model for malaria-HIV co-infection transmission and control, in which malaria treatment and insecticide-treated nets are incorporated. The existence of a backward bifurcation is established analytically, and the occurrence of such backward bifurcation is influenced by disease-induced mortality, insecticide-treated bed-net coverage and malaria treatment parameters. To further assess the impact of malaria treatment and insecticide-treated bed-net coverage, we formulate an optimal control problem with malaria treatment and insecticide-treated nets as control functions. Using reasonable parameter values, numerical simulations of the optimal control suggest the possibility of eliminating malaria and reducing HIV prevalence significantly, within a short time horizon.

We formulate an immuno-epidemiological model of coupled “within-host” model of ODEs and “between-host” model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the “between-host” model is established, and an explicit expression for the basic reproduction number of the “between-host” model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained.