Analysis of a non-integer order mathematical model for double strains of dengue and COVID-19 co-circulation using an efficient finite-difference method.

An efficient finite difference approach is adopted to analyze the solution of a novel fractional-order mathematical model to control the co-circulation of double strains of dengue and COVID-19. The model is primarily built on a non-integer Caputo fractional derivative. The famous fixed-point theorem developed by Banach is employed to ensure that the solution of the formulated model exists and is ultimately unique. The model is examined for stability around the infection-free equilibrium point analysis, and it was observed that it is stable (asymptotically) when the maximum reproduction number is strictly below unity. Furthermore, global stability analysis of the disease-present equilibrium is conducted via the direct Lyapunov method. The non-standard finite difference (NSFD) approach is adopted to solve the formulated model. Furthermore, numerical experiments on the model reveal that the trajectories of the infected compartments converge to the disease-present equilibrium when the basic reproduction number ([Formula: see text]) is greater than one and disease-free equilibrium when the basic reproduction number is less than one respectively. This convergence is independent of the fractional orders and assumed initial conditions. The paper equally emphasized the outcome of altering the fractional orders, infection and recovery rates on the disease patterns. Similarly, we also remarked the importance of some key control measures to curtail the co-spread of double strains of dengue and COVID-19.

Modeling SARS-CoV-2 and HBV co-dynamics with optimal control.

Clinical reports have shown that chronic hepatitis B virus (HBV) patients co-infected with SARS-CoV-2 have a higher risk of complications with liver disease than patients without SARS-CoV-2. In this work, a co-dynamical model is designed for SARS-CoV-2 and HBV which incorporates incident infection with the dual diseases. Existence of boundary and co-existence endemic equilibria are proved. The occurrence of backward bifurcation, in the absence and presence of incident co-infection, is investigated through the proposed model. It is noted that in the absence of incident co-infection, backward bifurcation is not observed in the model. However, incident co-infection triggers this phenomenon. For a special case of the study, the disease free and endemic equilibria are shown to be globally asymptotically stable. To contain the spread of both infections in case of an endemic situation, the time dependent controls are incorporated in the model. Also, global sensitivity analysis is carried out by using appropriate ranges of the parameter values which helps to assess their level of sensitivity with reference to the reproduction numbers and the infected components of the model. Finally, numerical assessment of the control system using various intervention strategies is performed, and reached at the conclusion that enhanced preventive efforts against incident co-infection could remarkably control the co-circulation of both SARS-CoV-2 and HBV.

The stability analysis of a co-circulation model for COVID-19, dengue, and zika with nonlinear incidence rates and vaccination strategies.

This paper aims to study the impacts of COVID-19 and dengue vaccinations on the dynamics of zika transmission by developing a vaccination model with the incorporation of saturated incidence rates. Analyses are performed to assess the qualitative behavior of the model. Carrying out bifurcation analysis of the model, it was concluded that co-infection, super-infection and also re-infection with same or different disease could trigger backward bifurcation. Employing well-formulated Lyapunov functions, the model's equilibria are shown to be globally stable for a certain scenario. Moreover, global sensitivity analyses are performed out to assess the impact of dominant parameters that drive each disease's dynamics and its co-infection. Model fitting is performed on the actual data for the state of Amazonas in Brazil. The fittings reveal that our model behaves very well with the data. The significance of saturated incidence rates on the dynamics of three diseases is also highlighted. Based on the numerical investigation of the model, it was observed that increased vaccination efforts against COVID-19 and dengue could positively impact zika dynamics and the co-spread of triple infections.

Adaptive changes in sexual behavior in the high-risk population in response to human monkeypox transmission in Canada can help control the outbreak: Insights from a two-group, two-route epidemic model.

Monkeypox, a zoonotic disease, is emerging as a potential sexually transmitted infection/disease, with underlying transmission mechanisms still unclear. We devised a risk-structured, compartmental model, incorporating sexual behavior dynamics. We compared different strategies targeting the high-risk population: a scenario of control policies geared toward the use of condoms and/or sexual abstinence (robust control strategy) with risk compensation behavior change, and a scenario of control strategies with behavior change in response to the doubling rate (adaptive control strategy). Monkeypox's basic reproduction number is 1.464, 0.0066, and 1.461 in the high-risk, low-risk, and total populations, respectively, with the high-risk group being the major driver of monkeypox spread. Policies imposing condom use or sexual abstinence need to achieve a 35% minimum compliance rate to stop further transmission, while a combination of both can curb the spread with 10% compliance to abstinence and 25% to condom use. With risk compensation, the only option is to impose sexual abstinence by at least 35%. Adaptive control is more effective than robust control where the daily sexual contact number is reduced proportionally and remains constant thereafter, shortening the time to epidemic peak, lowering its size, facilitating disease attenuation, and playing a key role in controlling the current outbreak.

Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2.

Several mathematical models have been developed to investigate the dynamics SARS-CoV-2 and its different variants. Most of the multi-strain SARS-CoV-2 models do not capture an important and more realistic feature of such models known as randomness. As the dynamical behavior of most epidemics, especially SARS-CoV-2, is unarguably influenced by several random factors, it is appropriate to consider a stochastic vaccination co-infection model for two strains of SARS-CoV-2. In this work, a new stochastic model for two variants of SARS-CoV-2 is presented. The conditions of existence and the uniqueness of a unique global solution of the stochastic model are derived. Constructing an appropriate Lyapunov function, the conditions for the stochastic system to fluctuate around endemic equilibrium of the deterministic system are derived. Stationary distribution and ergodicity for the new co-infection model are also studied. Numerical simulations are carried out to validate theoretical results. It is observed that when the white noise intensities are larger than certain thresholds and the associated stochastic reproduction numbers are less than unity, both strains die out and go into extinction with unit probability. More-over, it is observed that, for weak white noise intensities, the solution of the stochastic system fluctuates around the endemic equilibrium (EE) of the deterministic model. Frequency distributions are also studied to show random fluctuations due to stochastic white noise intensities. The results presented herein also reveal the impact of vaccination in reducing the co-circulation of SARS-CoV-2 variants within a given population.

Knowing the unknown: The underestimation of monkeypox cases. Insights and implications from an integrative review of the literature.

Monkeypox is an emerging zoonotic disease caused by the monkeypox virus, which is an infectious agent belonging to the genus Orthopoxvirus. Currently, commencing from the end of April 2022, an outbreak of monkeypox is ongoing, with more than 43,000 cases reported as of 23 August 2022, involving 99 countries and territories across all the six World Health Organization (WHO) regions. On 23 July 2022, the Director-General of the WHO declared monkeypox a global public health emergency of international concern (PHEIC), since the outbreak represents an extraordinary, unusual, and unexpected event that poses a significant risk for international spread, requiring an immediate, coordinated international response. However, the real magnitude of the burden of disease could be masked by failures in ascertainment and under-detection. As such, underestimation affects the efficiency and reliability of surveillance and notification systems and compromises the possibility of making informed and evidence-based policy decisions in terms of the adoption and implementation of ad hoc adequate preventive measures. In this review, synthesizing 53 papers, we summarize the determinants of the underestimation of sexually transmitted diseases, in general, and, in particular, monkeypox, in terms of all their various components and dimensions (under-ascertainment, underreporting, under-detection, under-diagnosis, misdiagnosis/misclassification, and under-notification).

An optimal control model for COVID-19, zika, dengue, and chikungunya co-dynamics with reinfection.

The co-circulation of different emerging viral diseases is a big challenge from an epidemiological point of view. The similarity of symptoms, cases of virus co-infection, and cross-reaction can mislead in the diagnosis of the disease. In this article, a new mathematical model for COVID-19, zika, chikungunya, and dengue co-dynamics is developed and studied to assess the impact of COVID-19 on zika, dengue, and chikungunya dynamics and vice-versa. The local and global stability analyses are carried out. The model is shown to undergo a backward bifurcation under a certain condition. Global sensitivity analysis is also performed on the parameters of the model to determine the most dominant parameters. If the zika-related reproduction number ℛ 0Z is used as the response function, then important parameters are: the effective contact rate for vector-to-human transmission of zika ( ß 2 h , which is positively correlated), the human natural death rate ( ϑ h , positively correlated), and the vector recruitment rate ( Ψ v , also positively correlated). In addition, using the class of individuals co-infected with COVID-19 and zika ( ℐ CZ h ) as response function, the most dominant parameters are: the effective contact rate for COVID-19 transmission ( ß 1 , positively correlated), the effective contact rate for vector-to-human transmission of zika ( ß 2 h , positively correlated). To control the co-circulation of all the diseases adequately under an endemic setting, time dependent controls in the form of COVID-19, zika, dengue, and chikungunya preventions are incorporated into the model and analyzed using the Pontryagin's principle. The model is fitted to real COVID-19, zika, dengue, and chikungunya datasets for Espirito Santo (a city with the co-circulation of all the diseases), in Brazil and projections made for the cumulative cases of each of the diseases. Through simulations, it is shown that COVID-19 prevention could greatly reduce the burden of co-infections with zika, dengue, and chikungunya. The negative impact of the COVID-19 pandemic on the control of the arbovirus diseases is also highlighted. Furthermore, it is observed that prevention controls for zika, dengue, and chikungunya can significantly reduce the burden of co-infections with COVID-19.

Assessing the impact of SARS-CoV-2 infection on the dynamics of dengue and HIV via fractional derivatives.

A new non-integer order mathematical model for SARS-CoV-2, Dengue and HIV co-dynamics is designed and studied. The impact of SARS-CoV-2 infection on the dynamics of dengue and HIV is analyzed using the tools of fractional calculus. The existence and uniqueness of solution of the proposed model are established employing well known Banach contraction principle. The Ulam-Hyers and generalized Ulam-Hyers stability of the model is also presented. We have applied the Laplace Adomian decomposition method to investigate the model with the help of three different fractional derivatives, namely: Caputo, Caputo-Fabrizio and Atangana-Baleanu derivatives. Stability analyses of the iterative schemes are also performed. The model fitting using the three fractional derivatives was carried out using real data from Argentina. Simulations were performed with each non-integer derivative and the results thus obtained are compared. Furthermore, it was concluded that efforts to keep the spread of SARS-CoV-2 low will have a significant impact in reducing the co-infections of SARS-CoV-2 and dengue or SARS-COV-2 and HIV. We also highlighted the impact of three different fractional derivatives in analyzing complex models dealing with the co-dynamics of different diseases.

Backward bifurcation and optimal control in a co-infection model for SARS-CoV-2 and ZIKV.

In co-infection models for two diseases, it is mostly claimed that, the dynamical behavior of the sub-models usually predict or drive the behavior of the complete models. However, under a certain assumption such as, allowing incident co-infection with both diseases, we have a different observation. In this paper, a new mathematical model for SARS-CoV-2 and Zika co-dynamics is presented which incorporates incident co-infection by susceptible individuals. It is worth mentioning that the assumption is missing in many existing co-infection models. We shall discuss the impact of this assumption on the dynamics of a co-infection model. The model also captures sexual transmission of Zika virus. The positivity and boundedness of solution of the proposed model are studied, in addition to the local asymptotic stability analysis. The model is shown to exhibit backward bifurcation caused by the disease-induced death rates and parameters associated with susceptibility to a second infection by those singly infected. Using Lyapunov functions, the disease free and endemic equilibria are shown to be globally asymptotically stable for R 0 1 , respectively. To manage the co-circulation of both infections effectively, under an endemic setting, time dependent controls in the form of SARS-CoV-2, Zika and co-infection prevention strategies are incorporated into the model. The simulations show that SARS-CoV-2 prevention could greatly reduce the burden of co-infections with Zika. Furthermore, it is also shown that prevention controls for Zika can significantly decrease the burden of co-infections with SARS-CoV-2.

A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus.

Fractional differential equations are beginning to gain widespread usage in modeling physical and biological processes. It is worth mentioning that the standard mathematical models of integer-order derivatives, including nonlinear models, do not constitute suitable framework in many cases. In this work, a mathematical model for COVID-19 and Hepatitis B Virus (HBV) co-interaction is developed and studied using the Atangana-Baleanu fractional derivative. The necessary conditions of the existence and uniqueness of the solution of the proposed model are studied. The local stability analysis is carried out when the reproduction number is less than one. Using well constructed Lyapunov functions, the disease free and endemic equilibria are proven to be globally asymptotically stable under certain conditions. Employing fixed point theory, the stability of the iterative scheme to approximate the solution of the model is discussed. The model is fitted to real data from the city of Wuhan, China, and important parameters relating to each disease and their co-infection, are estimated from the fitting. The approximate solutions of the model are compared using the integer and fractional order derivatives. The impact of the fractional derivative on the proposed model is also highlighted. The results proven in this paper illustrate that HBV and COVID-19 transmission rates can greatly impact the dynamics of the co-infection of both diseases. It is concluded that to control the co-circulation of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.

Analysis of COVID-19 and comorbidity co-infection model with optimal control.

In this work, we develop and analyze a mathematical model for the dynamics of COVID-19 with re-infection in order to assess the impact of prior comorbidity (specifically, diabetes mellitus) on COVID-19 complications. The model is simulated using data relevant to the dynamics of the diseases in Lagos, Nigeria, making predictions for the attainment of peak periods in the presence or absence of comorbidity. The model is shown to undergo the phenomenon of backward bifurcation caused by the parameter accounting for increased susceptibility to COVID-19 infection by comorbid susceptibles as well as the rate of reinfection by those who have recovered from a previous COVID-19 infection. Simulations of the cumulative number of active cases (including those with comorbidity), at different reinfection rates, show infection peaks reducing with decreasing reinfection of those who have recovered from a previous COVID-19 infection. In addition, optimal control and cost-effectiveness analysis of the model reveal that the strategy that prevents COVID-19 infection by comorbid susceptibles is the most cost-effective of all the control strategies for the prevention of COVID-19.