Transmission dynamics of SARS-CoV-2: A modeling analysis with high-and-moderate risk populations

Impacts of optimal control strategies on the HBV and COVID-19 co-epidemic spreading dynamics

Different cross-sectional and clinical research studies investigated that chronic HBV infected individuals' co-epidemic with COVID-19 infection will have more complicated liver infection than HBV infected individuals in the absence of COVID-19 infection. The main objective of this study is to investigate the optimal impacts of four time dependent control strategies on the HBV and COVID-19 co-epidemic transmission using compartmental modeling approach. The qualitative analyses of the model investigated the model solutions non-negativity and boundedness, calculated all the models effective reproduction numbers by applying the next generation operator approach, computed all the models disease-free equilibrium point (s) and endemic equilibrium point (s) and proved their local stability, shown the phenomenon of backward bifurcation by applying the Center Manifold criteria. By applied the Pontryagin's Maximum principle, the study re-formulated and analyzed the co-epidemic model optimal control problem by incorporating four time dependent controlling variables. The study also carried out numerical simulations to verify the model qualitative results and to investigate the optimal impacts of the proposed optimal control strategies. The main finding of the study reveals that implementation of protections, COVID-19 vaccine, and treatment strategies simultaneously is the most effective optimal control strategy to tackle the HBV and COVID-19 co-epidemic spreading in the community.

The analysis of a new fractional model to the Zika virus infection with mutant

We present a new mathematical model to analyze the dynamics of the Zika virus (ZV) disease with the mutant under the real confirmed cases in Colombia. We give the formulation of the model initially in integer order derivative and then extend it to a fractional order system in the sense of the Mittag-Leffler kernel. We study the properties of the model in the Mittag-Leffler kernel and establish the result. The basic reproduction of the fractional system is computed. The equilibrium points of the Zika virus model are obtained and found that the endemic equilibria exist when the threshold is greater than unity. Further, we show that the model does not possess the backward bifurcation phenomenon. The numerical procedure to solve the problem using the Atangana-Baleanu derivative is shown using the newly established numerical scheme. We consider the real cases of the Zika virus in Colombia outbreak are considered and simulate the model using the nonlinear least square curve fit and computed the basic reproduction number R 0 = 0.4942 , whereas in previous work (Alzahrani et al., 2021) [1], the authors computed the basic reproduction number R 0 = 0.5447 . This is due to the fact that our work in the present paper provides better fitting to the data when using the fractional order model, and indeed the result regarding the data fitting using the fractional model is better than integer order model. We give a sensitivity analysis of the parameters involved in the basic reproduction number and show them graphically. The results obtained through the present numerical method converge to its equilibrium for the fractional order, indicating the proposed scheme's reliability.

A dynamical analysis and numerical simulation of COVID-19 and HIV/AIDS co-infection with intervention strategies

HIV/AIDS-COVID-19 co-infection is a major public health concern especially in developing countries of the world. This paper presents HIV/AIDS-COVID-19 co-infection to investigate the impact of interventions on its transmission using ordinary differential equation. In the analysis of the model, the solutions are shown to be non-negative and bounded, using next-generation matrix approach the basic reproduction numbers are computed, sufficient conditions for stabilities of equilibrium points are established. The sensitivity analysis showed that transmission rates are the most sensitive parameters that have direct impact on the basic reproduction numbers and protection and treatment rates are more sensitive and have indirect impact to the basic reproduction numbers. Numerical simulations shown that some parameter effects on the transmission of single infections as well as co-infection, and applying the protection rates and treatment rates have effective roles to minimize and also to eradicate the HIV/AIDS-COVID-19 co-infection spreading in the community.

Analysis of HBV and COVID-19 Coinfection Model with Intervention Strategies

Coinfection of hepatitis B virus (HBV) and COVID-19 is a common public health problem throughout some nations in the world. In this study, a mathematical model for hepatitis B virus (HBV) and COVID-19 coinfection is constructed to investigate the effect of protection and treatment mechanisms on its spread in the community. Necessary conditions of the proposed model nonnegativity and boundedness of solutions are analyzed. We calculated the model reproduction numbers and carried out the local stabilities of disease-free equilibrium points whenever the associated reproduction number is less than unity. Using the well-known Castillo-Chavez criteria, the disease-free equilibrium points are shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Sensitivity analysis proved that the most influential parameters are transmission rates. Moreover, we carried out numerical simulation and shown results: some parameters have high spreading effect on the disease transmission, single infections have great impact on the coinfection transmission, and using protections and treatments simultaneously is the most effective strategy to minimize and also to eradicate the HBV and COVID-19 coinfection spreading in the community. It is concluded that to control the transmission of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.

A vigorous study of fractional order mathematical model for SARS-CoV-2 epidemic with Mittag-Leffler kernel

SARS-CoV-2 and its variants have been investigated using a variety of mathematical models. In contrast to multi-strain models, SARS-CoV-2 models exhibit a memory effect that is often overlooked and more realistic. Atangana-Baleanu’s fractional-order operator is discussed in this manuscript for the analysis of the transmission dynamics of SARS-CoV-2. We investigated the transmission mechanism of the SARS-CoV-2 virus using the non-local Atangana-Baleanu fractional-order approach taking into account the different phases of infection and transmission routes. Using conventional ordinary derivative operators, our first step will be to develop a model for the proposed study. As part of the extension, we will incorporate fractional order derivatives into the model where the used operator is the fractional order operator of order Ψ1. Additionally, some basic aspects of the proposed model are examined in addition to calculating the reproduction number and determining the possible equilibrium. Stability analysis of the model is conducted to determine the necessary equilibrium conditions as they are also required in developing a numerical setup. Utilizing the theory of nonlinear functional analysis, for the model, Ulam-Hyers’ stability is established. We present a numerical scheme based on Newton’s polynomial in order to set up an iterative algorithm for the proposed ABC system. The application of this scheme to a variety of values of Φ1 indicates that there is a relationship between infection dynamics and the derivative’s order. We present further simulations which demonstrate the importance and cruciality of different parameters, as well as their effect on the dynamics and administer the disease. Furthermore, this study will provide a better understanding of the mechanisms underlying contagious diseases, thus supporting the development of policies to control them.

Accessibility of the three-year comprehensive prevention and control of brucellosis in Ningxia: a mathematical modeling study

BACKGROUND

Brucellosis is a chronic zoonotic disease, and Ningxia is one of the high prevalence regions in China. To mitigate the spread of brucellosis, the government of Ningxia has implemented a comprehensive prevention and control plan (2022-2024). It is meaningful to quantitatively evaluate the accessibility of this strategy.

METHODS

Based on the transmission characteristics of brucellosis in Ningxia, we propose a dynamical model of sheep-human-environment, which coupling with the stage structure of sheep and indirect environmental transmission. We first calculate the basic reproduction number [Formula: see text] and use the model to fit the data of human brucellosis. Then, three widely applied control strategies of brucellosis in Ningxia, that is, slaughtering of sicked sheep, health education to high risk practitioners, and immunization of adult sheep, are evaluated.

RESULTS

The basic reproduction number is calculated as [Formula: see text], indicating that human brucellosis will persist. The model has a good alignment with the human brucellosis data. The quantitative accessibility evaluation results show that current brucellosis control strategy may not reach the goal on time. "Ningxia Brucellosis Prevention and Control Special Three-Year Action Implementation Plan (2022-2024)" will be achieved in 2024 when increasing slaughtering rate [Formula: see text] by 30[Formula: see text], increasing health education to reduce [Formula: see text] to 50[Formula: see text], and an increase of immunization rate of adult sheep [Formula: see text] by 40[Formula: see text].

CONCLUSION

The results demonstrate that the comprehensive control measures are the most effective for brucellosis control, and it is necessary to further strengthen the multi-sectoral joint mechanism and adopt integrated measures to prevention and control brucellosis. These results can provide a reliable quantitative basis for further optimizing the prevention and control strategy of brucellosis in Ningxia.

Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV/AIDS and COVID-19 co-infection in the community under consideration of the study.

Mathematical analysis of the transmission dynamics of COVID-19 infection in the presence of intervention strategies

The novel Coronavirus (COVID-19) infection has become a global public health issue, and it has been a cause for morbidity and mortality of more people throughout the world. In this paper, we investigated the impacts of vaccination, other protection measures, home quarantine with treatment, and hospital quarantine with treatment strategies simultaneously using a deterministic mathematical modelling approach. No one has considered these intervention strategies simultaneously in his/her modelling approach. We examined all the qualitative properties of the model such as the positivity and boundedness of the model solutions, the disease-free and endemic equilibrium points, the effective reproduction number using next-generation matrix method, local stabilities of equilibrium points using the Routh-Hurwitz method. Using the Centre Manifold criteria, we have shown the existence of backward bifurcation whenever the COVID-19 effective reproduction number is less than unity. Moreover, we have analysed both sensitivity and numerical simulation using parameter values taken from published literature. The numerical results show that the transmission rate is the most sensitive parameter we have to control. Also vaccination, other protection measures, home quarantine with treatment, and hospital quarantine with treatment have great effects to minimize the COVID-19 transmission in the community.

Unravelling the dynamics of Lassa fever transmission with differential infectivity: Modeling analysis and control strategies

Epidemic models have been broadly used to comprehend the dynamic behaviour of emerging and re-emerging infectious diseases, predict future trends, and assess intervention strategies. The symptomatic and asymptomatic features and environmental factors for Lassa fever (LF) transmission illustrate the need for sophisticated epidemic models to capture more vital dynamics and forecast trends of LF outbreaks within countries or sub-regions on various geographic scales. This study proposes a dynamic model to examine the transmission of LF infection, a deadly disease transmitted mainly by rodents through environment. We extend prior LF models by including an infectious stage to mild and severe as well as incorporating environmental contributions from infected humans and rodents. For model calibration and prediction, we show that the model fits well with the LF scenario in Nigeria and yields remarkable prediction results. Rigorous mathematical computation divulges that the model comprises two equilibria. That is disease-free equilibrium, which is locally-asymptotically stable (LAS) when the basic reproduction number, $ {\mathcal{R}}_{0} $, is $ < 1 $; and endemic equilibrium, which is globally-asymptotically stable (GAS) when $ {\mathcal{R}}_{0} $ is $ > 1 $. We use time-dependent control strategy by employing Pontryagin's Maximum Principle to derive conditions for optimal LF control. Furthermore, a partial rank correlation coefficient is adopted for the sensitivity analysis to obtain the model's top rank parameters requiring precise attention for efficacious LF prevention and control.

A Mathematical Modeling Analysis of Racism and Corruption Codynamics with Numerical Simulation as Infectious Diseases

Racism and corruption are mind infections which affect almost all public and governmental sectors. However, we cannot find enough published literatures on mathematical model analyses of racism and corruption coexistence. In this study, we have contemplated the dynamics of racism and corruption coexistence in communities, using deterministic compartmental model to analyze and suggest proper control strategies to stakeholders. We used qualitative and comprehensive mathematical methods and analyzed both the racism model in the absence of corruption and the corruption model in the absence of racism. We have computed basic reproduction numbers by applying the next generation matrix method. The developed model has a disease-free equilibrium point that is locally asymptotically stable whenever the reproduction number is less than one. Additionally, we have done sensitivity analysis to observe the effect of the parameters on the incidence and transmission of the mind infections that deduce the transmission rates of both the racism and corruption are highly sensitive. The numerical simulation we have simulated showed that the endemic equilibrium point of racism and corruption coexistence model is locally asymptotically stable when max{ ℛ r, ℛ c} > 1, the effects of parameters on the basic reproduction numbers, and the effect of parameter on the infectious groups. Finally, the stakeholders must focus on minimizing the transmission rates and increasing the recovery (removed) rate for both racism and corruption action which can be considered prevention and controlling strategies.

Unravelling the dynamics of the COVID-19 pandemic with the effect of vaccination, vertical transmission and hospitalization

The coronavirus disease 2019 (COVID-19) is caused by a newly emerged virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), transmitted through air droplets from an infected person. However, other transmission routes are reported, such as vertical transmission. Here, we propose an epidemic model that considers the combined effect of vertical transmission, vaccination and hospitalization to investigate the dynamics of the virus's dissemination. Rigorous mathematical analysis of the model reveals that two equilibria exist: the disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number ( R 0 ) is less than 1 (unstable otherwise), and an endemic equilibrium, which is globally asymptotically stable when R 0 > 1 under certain conditions, implying the plausibility of the disease to spread and cause large outbreaks in a community. Moreover, we fit the model using the Saudi Arabia cases scenario, which designates the incidence cases from the in-depth surveillance data as well as displays the epidemic trends in Saudi Arabia. Through Caputo fractional-order, simulation results are provided to show dynamics behaviour on the model parameters. Together with the non-integer order variant, the proposed model is considered to explain various dynamics features of the disease. Further numerical simulations are carried out using an efficient numerical technique to offer additional insight into the model's dynamics and investigate the combined effect of vaccination, vertical transmission, and hospitalization. In addition, a sensitivity analysis is conducted on the model parameters against the R 0 and infection attack rate to pinpoint the most crucial parameters that should be emphasized in controlling the pandemic effectively. Finally, the findings suggest that adequate vaccination coupled with basic non-pharmaceutical interventions are crucial in mitigating disease incidences and deaths.

Transmission dynamics of COVID-19 pandemic with combined effects of relapse, reinfection and environmental contribution: A modeling analysis

Reinfection and reactivation of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have recently raised public health pressing concerns in the fight against the current pandemic globally. In this study, we propose a new dynamic model to study the transmission of the coronavirus disease 2019 (COVID-19) pandemic. The model incorporates possible relapse, reinfection and environmental contribution to assess the combined effects on the overall transmission dynamics of SARS-CoV-2. The model's local asymptotic stability is analyzed qualitatively. We derive the formula for the basic reproduction number ( R 0 ) and final size epidemic relation, which are vital epidemiological quantities that are used to reveal disease transmission status and guide control strategies. Furthermore, the model is validated using the COVID-19 reported situations in Saudi Arabia. Moreover, sensitivity analysis is examined by implementing a partial rank correlation coefficient technique to obtain the ultimate rank model parameters to control or mitigate the pandemic effectively. Finally, we employ a standard Euler technique for numerical simulations of the model to elucidate the influence of some crucial parameters on the overall transmission dynamics. Our results highlight that contact rate, hospitalization rate, and reactivation rate are the fundamental parameters that need particular emphasis for the prevention, mitigation and control.

Why Controlling the Asymptomatic Infection Is Important: A Modelling Study with Stability and Sensitivity Analysis

The large proportion of asymptomatic patients is the major cause leading to the COVID-19 pandemic which is still a significant threat to the whole world. A six-dimensional ODE system (SEIAQR epidemical model) is established to study the dynamics of COVID-19 spreading considering infection by exposed, infected, and asymptomatic cases. The basic reproduction number derived from the model is more comprehensive including the contribution from the exposed, infected, and asymptomatic patients. For this more complex six-dimensional ODE system, we investigate the global and local stability of disease-free equilibrium, as well as the endemic equilibrium, whereas most studies overlooked asymptomatic infection or some other virus transmission features. In the sensitivity analysis, the parameters related to the asymptomatic play a significant role not only in the basic reproduction number R0. It is also found that the asymptomatic infection greatly affected the endemic equilibrium. Either in completely eradicating the disease or achieving a more realistic goal to reduce the COVID-19 cases in an endemic equilibrium, the importance of controlling the asymptomatic infection should be emphasized. The three-dimensional phase diagrams demonstrate the convergence point of the COVID-19 spreading under different initial conditions. In particular, massive infections will occur as shown in the phase diagram quantitatively in the case R0>1. Moreover, two four-dimensional contour maps of Rt are given varying with different parameters, which can offer better intuitive instructions on the control of the pandemic by adjusting policy-related parameters.

How Important Is Behavioral Change during the Early Stages of the COVID-19 Pandemic? A Mathematical Modeling Study

How important is the speed and intensity of behavioral change due to government policies, such as enhanced social distancing or lockdown, when an emerging infectious disease occurs? In this study, we introduce a deterministic SEIR model considering the behavior-changed susceptible group to investigate the effect of the speed and intensity of behavioral change on the transmission dynamics of COVID-19. We used epidemiological data from South Korea and Italy for the simulation study, because South Korea and Italy were the first countries to report an outbreak of COVID-19 after China and the prevention and response policy of each government were similar during the first outbreak of COVID-19. Simulation results showed that it took approximately twenty fewer days in Korea than in Italy until 90% of susceptible individuals changed their behavior during the first outbreak. It was observed that the behavior-changed susceptible individuals reduced the COVID-19 transmission rate by up to 93% in Korea and 77% in Italy. Furthermore, if the intensity and speed of behavioral change in Italy were the same as in Korea, the expected number of cumulative confirmed cases would have been reduced by approximately 95%, from 210,700 to 10,700, until the end of the lockdown period. We assumed that behavioral change is influenced by the number of confirmed cases and does not take into account social and cultural differences, as well as the state of the healthcare system, between the two countries. Our mathematical modeling showed how important the high intensity and fast speed of behavioral change to reduce the number of confirmed cases in the early period of an epidemic are.