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In this work, we present a deterministic model to examine how socioeconomic levels affect the co-dynamics of COVID-19 and cholera in the Haitian community. The threshold quantities called the basic and control reproduction numbers of both diseases were obtained by using the next-generation matrix method. To validate the model’s ability to predict a realistic result, each respective sub-model was fitted using the reported number of COVID-19 cases from March 20, 2020 to June 25, 2023 and the reported number of cholera cases from October 8, 2022 to August 26, 2023 from Haiti. A numerical simulation was performed to investigate the impact of socioeconomic levels on the threshold quantities and the projected infected cases of each disease. The overall result shows that, in comparison to medium or low socioeconomic levels, a high socioeconomic level lowers the threshold reproduction number more efficiently. This suggests that the burden of COVID-19 and cholera would decrease if Haiti’s socioeconomic status was raised to a better standard and the diseases’ related reproduction numbers were kept below the disease-free thresholds. Additionally, our results show that improving socioeconomic status is essential to reducing the number of predicted COVID-19 and cholera cases among Haitians. Our results also established that cholera disease would dominate in the Haiti population and drive COVID-19 into extinction when they are both at their endemic equilibria (i.e., cholera will dominate when ${{ℛ}}_1>1$ and ${{ℛ}}_2>1$). However, for COVID-19 to dominate and drive cholera into extinction in the Haiti population, only COVID-19 must be in an endemic state (i.e., COVID-19 will dominate when ${{ℛ}}_1>1$ and ${{ℛ}}_2<1$). Based on the study’s findings, the government and policymakers of Haiti were advised to ensure that the country’s socioeconomic status is improved in order to lower the population’s burden of disease.

Human Immunodeficiency Virus type-1 (HIV-1) fuels the pathogenesis of Mycobacterium tuberculosis (Mtb) in humans. We develop a mathematical model in an attempt to understand the immune mechanisms that are involved during the co-infection of Mtb and HIV-1. Our study reveals that infection of an Mtb infected individual with HIV-1 results in fast development of active TB. The mathematical model analysis and simulations show that Mtb infection is linked to HIV infection through macrophages and CD4+ T cells. The study shows that depletion of macrophages and CD4+ T cells by HIV-1 worsens the picture of Mtb infection and in-turn Mtb infection affects the progression of HIV-1 infection since it is also capable of inducing rapid replication of HIV. Our analytical and numerical simulations show that macrophages are a potential reservoir of HIV particles during HIV-1 infection. Co-infection simulations reveal that co-infection exacerbates more the pathogen that caused the first infection. Simulations also show that co-infection disease progression patterns converge to a similar trend after a considerable time interval irrespective of which pathogen first caused infection and the second pathogen that caused co-infection. This work suggests directions for further studies and potential treatment strategies.

Infection with the hepatitis C virus (HCV) is the most common coinfection in people with the human immunodeficiency virus (HIV), and hepatitis C is categorized as an HIV-related illness. The study of the joint dynamics of HIV and HCV present formidable mathematical challenges in spite the fact that they share similar routes of transmission. A deterministic model for the co-interaction of HCV and HIV in a community is presented and rigorously analyzed. The disease-free equilibrium is shown to be locally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than the unity. The Centre Manifold theory is used to show that the HCV only and HIV/AIDS only endemic equilibria are locally asymptotically stable when their associated reproduction numbers are greater than the unity. We compute two coexistence thresholds for the stability of boundary equilibria. Numerical results are presented to validate analytical results.

In this paper, a mathematical model for malaria-dysentery co-infection was formulated in order to study and examine its dynamic relationship in the presence of malaria and dysentery preventive and treatment measures. First, analysis of the single infection steady states was done and then the basic reproduction number was obtained. Furthermore, investigation into the existence and stability of equilibria carried out. The single infection models were found to exhibit the possibility of backward bifurcation. Thereafter, the impact of malaria on the dynamics of dysentery is further investigated. Second, incorporating time-dependent controls, using Pontryagin’s Maximum Principle, the necessary conditions for the optimal control of the disease was derived. It is found that malaria infection may be associated with an increased risk of dysentery. Also, that dysentery infection may be associated with an increased risk for malaria. Therefore, to effectively control malaria, the malaria intervention strategies by policy makers must at the same time it also includes effective prevention and control measures for dysentery. Policy makers should take efforts on preventive strategies in combating dysentery and malaria.

Currently, more than 600 million people worldwide are diagnosed with COVID-19, while the implication of Tuberculosis cannot be ignored. The combination of COVID-19 and Tuberculosis exacerbates the catastrophe, dealing a serious blow to the healthcare system. This paper addresses how to develop effective and reasonable programs to combat the spread of COVID-19 and Tuberculosis in the absence of Tuberculosis medical resources, as well as exploring the impact of medical resources on optimal control implementation. Therefore, a co-infection dynamic of COVID-19 and Tuberculosis is constructed and analyzed. In order to investigate approaches to mitigate the disease transmission, a comprehensive and integrated study including sensitivity analysis, optimal control design and cost-effectiveness analysis is then performed. The simulation results illustrate that, the combination of the three control measures effectively achieves a win-win result in economic and epidemiological terms. In addition, the impact of Tuberculosis medical resources is highlighted, and the study shows that an appropriate increase in the medical resource supply for Tuberculosis during optimal control can have a stronger inhibitory effect on co-infection. Finally, based on the actual data, the model is validated by fitting the cumulative confirmed case curves of the two diseases.

Porcine deltacoronavirus (PDCoV) causes clinical symptoms characterized by severe diarrhea and vomiting in neonatal piglets and pregnant sows, which is similar to those resulted from transmissible gastroenteritis coronavirus (TGEV) and porcine epidemic diarrhea virus (PEDV). Since PEDV was considered as the dominant enteric virus all round the world, PDCoV has been unwittingly overlooked due to its indistinguishable clinical signs with other porcine coronaviruses and relatively low death rates in the pig farm. Specimens which have been previously performed for the detection of PEDV in Animal Disease and Diagnostic Center, National Pingtung University of Science and Technology (NPUST) from January 5, 2015 to January 11, 2016 were examined by a novel universal probe library (UPL) probe-based real-time polymerase chain reaction (PCR). A total of 527 clinical specimens from pigs with diarrhea suspected were examined for PDCoV. Positive rates of PDCoV in small intestine and rectal swab were 4.3% (13/305) and 1.8% (4/222), respectively. Collectively, as to the total specimens, the detection rate is 3.2% (17/527). Our results provide development of a UPL probe-based real-time PCR assay and retrospective investigation of potentially circulating PDCoVs in the field in the whole 2015 and early 2016.

A model which incorporates some of the basic epidemiological features of the co-dynamics of malaria and tuberculosis (TB) is formulated and the effectiveness of current intervention strategies of these two diseases is analyzed. The malaria-only and TB-only models are considered first. Global stability disease-free steady states of the two sub-models does not hold due to the co-existence of stable disease-free with stable endemic equilibria, a phenomenon known as backward bifurcation. The dynamics of the dual malaria–TB model with intervention strategies are also analyzed. Numerical simulations of the malaria–TB model are carried out to determine whether the two diseases can co-exist. Lastly, sensitivity analysis on key parameters that drive the disease dynamics is performed in order to identify their relative importance to disease transmission.

In this paper, a nonlinear population model for HIV-TB co-infection has been proposed. The model is incorporated with the effect of early and late initiation of HIV treatment in co-infectives already on TB treatment, on the occurrence of Immune Reconstitution Inflammatory syndrome (IRIS). A 15-dimensional (15D) mathematical model has been developed in this study. We begin with considering constant treatment rates and thereafter, proceed to time-dependent treatment rates for co-infectives as control parameters. The basic reproduction number, a threshold quantity, corresponding to each HIV and TB sub-model has been computed in case of constant controls. With constant values of control parameters, mathematical analysis shows the existence and local stability of the disease-free equilibrium point and the endemic equilibrium point for the model. Together with time-dependent parameters, an optimal control problem is introduced and solved using Pontryagin’s maximum principle with an objective to minimize the number of infectives and disease induced deaths along with the cost of treatment. Numerical simulations are performed to examine the effect of reproduction numbers on control profiles and to identify, the ideal combination of treatment strategies which provides minimum burden on a society. Numerical results imply that if both HIV and TB are endemic in the population, then in order to bring in minimum burden from the co-infection, optimal control efforts must be enforced rather than constant treatment rate.

A co-infection model for human papillomavirus (HPV) and syphilis with cost-effectiveness optimal control analysis is developed and presented. The full co-infection model is shown to undergo the phenomenon of backward bifurcation when a certain condition is satisfied. The global asymptotic stability of the disease-free equilibrium of the full model is shown not to exist when the associated reproduction number is less than unity. The existence of endemic equilibrium of the syphilis-only sub-model is shown to exist and the global asymptotic stability of the disease-free and endemic equilibria of the syphilis-only sub-model was established, for a special case. Sensitivity analysis is also carried out on the parameters of the model. Using the syphilis associated reproduction number, ${{ℛ}}_{0s}$, as the response function, it is observed that the five-ranked parameters that drive the dynamics of the co-infection model are the demographic parameter $\mu$, the effective contact rate for syphilis transmission, ${\beta }_s$, the progression rate to late stage of syphilis ${\sigma }_2$, and syphilis treatment rates: ${\tau }_1$ and ${\tau }_2$ for co-infected individuals in compartments $H_i$ and $H_l$, respectively. Moreover, when the HPV associated reproduction number, ${{ℛ}}_{0h}$, is used as the response function, the five most dominant parameters that drive the dynamics of the model are the demographic parameter $\mu$, the effective contact rate for HPV transmission, ${\beta }_h$, the fraction of HPV infected who develop persistent HPV ${\rho }_1$, the fraction of individuals vaccinated against incident HPV infection $\varphi$ and the HPV vaccine efficacy ${\pi }_h$. Numerical simulations of the optimal control model showed that the optimal control strategy which implements syphilis treatment controls for singly infected individuals is the most cost-effective of all the control strategies in reducing the burden of HPV and syphilis co-infections.

It is very important to note that a mathematical model plays a key role in different infectious diseases. Here, we study the dynamical behaviors of both hepatitis B virus (HBV) and hepatitis C virus (HCV) with their co-infection. Actually, the purpose of this work is to show how the bi-therapy is effective and include an inhibitor for HCV infection with some treatments, which are frequently used against HBV. Local stability, global stability and its prevention from the community are studied. Mathematical models and optimality system of nonlinear DE are solved numerically by RK4. We use linearization, Lyapunov function and Pontryagin’s maximum principle for local stability, global stability and optimal control, respectively. Stability curves and basic reproductive number are plotted with and without control versus different values of parameters. This study shows that the infection will spread without control and can cover with treatment. The intensity of HBV/HCV co-infection is studied before and after optimal treatment. This represents a short drop after treatment. First, we formulate the model then find its equilibrium points for both. The models possess four distinct equilibria: HBV and HCV free, and endemic. For the proposed problem dynamics, we show the local as well as the global stability of the HBV and HCV. With the help of optimal control theory, we increase uninfected individuals and decrease the infected individuals. Three time-dependent variables are also used, namely, vaccination, treatment and isolation. Finally, optimal control is classified into optimality system, which we can solve with Runge–Kutta-order four method for different values of parameters. Finally, we will conclude the results for implementation to minimize the infected individuals.

Synergistic interaction between influenza and pneumonia is well established in the literature. In this study, we present a model for the transmission dynamics of co-infection with influenza and pneumococcal pneumonia, with the goal of assessing the effects of influenza co-infection on the transmission of pneumonia. We derive an expression for the basic reproductive number ${{ℛ}}_0=max({{ℛ}}_f,{{ℛ}}_p)$ where ${{ℛ}}_f$ and ${{ℛ}}_p$ are, respectively, the reproductive numbers for flu and pneumonia. We show that in the case ${{ℛ}}_f\le 1\le {{ℛ}}_p$, infection with influenza is driven to extinction while pneumonia is endemic, with the endemic state being globally asymptotically stable. The converse result holds in the case where ${{ℛ}}_p\le 1\le {{ℛ}}_f$. We also show the existence of the co-infection equilibrium. In this case, we show that the presence of co-infection results in a possible backward bifurcation in the system at ${{ℛ}}_0=1$; epidemiologically, this means that the spread of the infection will be harder to control. Numerical simulations are presented to verify the analytic results and gain further insights.

A Pneumonia and HIV/AIDS deterministic co-infection model is constructed and utilized to assess how the dynamics of Pneumonia and HIV/AIDS impact on each other. In order to summarize the analysis of Pneumonia and HIV/AIDS co-infection model, the analysis of Pneumonia and HIV/AIDS sub-models is undertaken. The basic reproduction numbers ${{ℛ}}_P^0$ for Pneumonia sub-model, ${{ℛ}}_H^0$ for HIV/AIDS sub-model and ${{ℛ}}_0$ for Pneumonia and HIV/AIDS co-infection model are computed, the results are then fielded to establish the local and global asymptotic stabilities of the corresponding models’ equilibrium points. Sensitivity analysis is done and results reveal that Pneumonia spreading rate, HIV spreading rate and treatment rates of the infected sub-populations are the most sensitive parameters. The model is further modified to incorporate intervention schemes, namely Pneumonia prevention, screening and treatment efforts, HIV/AIDS prevention, screening and treatment efforts in the form of time-dependent controls. Numerical simulations portray that prevention and treatment of both diseases averts the biggest numbers of co-infected individuals. However, in a situation when there are scarce resources to deploy all intervention schemes, a combination of treatment for both diseases become a scheme of choice in reducing the co-infection burden.