Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

Nonlinear optimal control strategies for a mathematical model of COVID-19 and influenza co-infection

Infectious diseases have remained one of humanity's biggest problems for decades. Multiple disease infections, in particular, have been shown to increase the difficulty of diagnosing and treating infected people, resulting in worsening human health. For example, the presence of influenza in the population is exacerbating the ongoing COVID-19 pandemic. We formulate and analyze a deterministic mathematical model that incorporates the biological dynamics of COVID-19 and influenza to effectively investigate the co-dynamics of the two diseases in the public. The existence and stability of the disease-free equilibrium of COVID-19-only and influenza-only sub-models are established by using their respective threshold quantities. The result shows that the COVID-19 free equilibrium is locally asymptotically stable when R C < 1 , whereas the influenza-only model, is locally asymptotically stable when R F < 1 . Furthermore, the existence of the endemic equilibria of the sub-models is examined while the conditions for the phenomenon of backward bifurcation are presented. A generalized analytical result of the COVID-19-influenza co-infection model is presented. We run a numerical simulation on the model without optimal control to see how competitive outcomes between-hosts and within-hosts affect disease co-dynamics. The findings established that disease competitive dynamics in the population are determined by transmission probabilities and threshold quantities. To obtain the optimal control problem, we extend the formulated model by including three time-dependent control functions. The maximum principle of Pontryagin was used to prove the existence of the optimal control problem and to derive the necessary conditions for optimum disease control. A numerical simulation was performed to demonstrate the impact of different combinations of control strategies on the infected population. The findings show that, while single and twofold control interventions can be used to reduce disease, the threefold control intervention, which incorporates all three controls, will be the most effective in reducing COVID-19 and influenza in the population.

Two strains and drug adherence: An HIV model in the paradigm of community transmission

A two-strain model, comprising of drug-sensitive and drug-resistant strains, is proposed for the dynamics of Human Immunodeficiency Virus (HIV) spread in a community. A treatment model is introduced by taking drug adherence into account. The treatment-free model is analyzed for the effect of treatment availability and drug adherence on disease dynamics. The analysis revealed that for the treatment-free model, at least one strain faces competitive exclusion, and co-existence of both strains is not possible. On the contrary, both strains may co-exist in presence of treatment. The analysis carried out was both local, as well as global. A comprehensive bifurcation analysis showed periodic behaviour and all solutions approached a stable limit cycle for a wide range of parametric values. Overall, we concluded that the treatment availability and drug adherence play a significant role in determining the dynamics of HIV spread. Numerical simulations are performed to validate the analytical results using MATLAB.

In silico design of recombinant multi-epitope vaccine against influenza A virus

Background

Influenza A virus is one of the leading causes of annual mortality. The emerging of novel escape variants of the influenza A virus is still a considerable challenge in the annual process of vaccine production. The evolution of vaccines ranks among the most critical successes in medicine and has eradicated numerous infectious diseases. Recently, multi-epitope vaccines, which are based on the selection of epitopes, have been increasingly investigated.

Results

This study utilized an immunoinformatic approach to design a recombinant multi-epitope vaccine based on a highly conserved epitope of hemagglutinin, neuraminidase, and membrane matrix proteins with fewer changes or mutate over time. The potential B cells, cytotoxic T lymphocytes (CTL), and CD4 T cell epitopes were identified. The recombinant multi-epitope vaccine was designed using specific linkers and a proper adjuvant. Moreover, some bioinformatics online servers and datasets were used to evaluate the immunogenicity and chemical properties of selected epitopes. In addition, Universal Immune System Simulator (UISS) in silico trial computational framework was run after influenza exposure and recombinant multi-epitope vaccine administration, showing a good immune response in terms of immunoglobulins of class G (IgG), T Helper 1 cells (TH1), epithelial cells (EP) and interferon gamma (IFN-g) levels. Furthermore, after a reverse translation (i.e., convertion of amino acid sequence to nucleotide one) and codon optimization phase, the optimized sequence was placed between the two EcoRV/MscI restriction sites in the PET32a⁺ vector.

Conclusions

The proposed “Recombinant multi-epitope vaccine” was predicted with unique and acceptable immunological properties. This recombinant multi-epitope vaccine can be successfully expressed in the prokaryotic system and accepted for immunogenicity studies against the influenza virus at the in silico level. The multi-epitope vaccine was then tested with the Universal Immune System Simulator (UISS) in silico trial platform. It revealed slight immune protection against the influenza virus, shedding the light that a multistep bioinformatics approach including molecular and cellular level is mandatory to avoid inappropriate vaccine efficacy predictions.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04581-6.

Towards a Mathematical Model for the Viral Progression in the Pharynx

In this work, a comprehensive model for the viral progression in the pharynx has been developed. This one-dimension model considers both Fickian diffusion and convective flow coupled with chemical reactions, such as virus population growth, infected and uninfected cell accumulation as well as virus clearance. The effect of a sterilizing agent such as an alcoholic solution on the viral progression in the pharynx was taken into account and a parametric analysis for the effect of kinetic rate parameters on virus propagation was made. Moreover, different conditions caused by further medical treatment, such as a decrease in virus yield per infected cell, were examined. It is shown that the infection fails to establish by decreasing the virus yield per infected cell. It is believed that this work could be used to further investigate the medical treatment of viral progression in the pharynx.

A Review of COVID-19 Modelling Strategies in Three Countries to Develop a Research Framework for Regional Areas

At the end of December 2019, an outbreak of COVID-19 occurred in Wuhan city, China. Modelling plays a crucial role in developing a strategy to prevent a disease outbreak from spreading around the globe. Models have contributed to the perspicacity of epidemiological variations between and within nations and the planning of desired control strategies. In this paper, a literature review was conducted to summarise knowledge about COVID-19 disease modelling in three countries-China, the UK and Australia-to develop a robust research framework for the regional areas that are urban and rural health districts of New South Wales, Australia. In different aspects of modelling, summarising disease and intervention strategies can help policymakers control the outbreak of COVID-19 and may motivate modelling disease-related research at a finer level of regional geospatial scales in the future.

SARS-CoV-2 coinfections: Could influenza and the common cold be beneficial?

The novel coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has rapidly spread around the world, causing serious illness and death and creating a heavy burden on the healthcare systems of many countries. Since the virus first emerged in late November 2019, its spread has coincided with peak circulation of several seasonal respiratory viruses, yet some studies have noted limited coinfections between SARS-CoV-2 and other viruses. We use a mathematical model of viral coinfection to study SARS-CoV-2 coinfections, finding that SARS-CoV-2 replication is easily suppressed by many common respiratory viruses. According to our model, this suppression is because SARS-CoV-2 has a lower growth rate (1.8/d) than the other viruses examined in this study. The suppression of SARS-CoV-2 by other pathogens could have implications for the timing and severity of a second wave.