Effective Reproduction Number Research Articles

Real-Time Epidemiology and Acute Care Need Monitoring and Forecasting for COVID-19 via Bayesian Sequential Monte Carlo-Leveraged Transmission Models.

COVID-19 transmission models have conferred great value in informing public health understanding, planning, and response. However, the pandemic also demonstrated the infeasibility of basing public health decision-making on transmission models with pre-set assumptions. No matter how favourably evidenced when built, a model with fixed assumptions is challenged by numerous factors that are difficult to predict. Ongoing planning associated with rolling back and re-instituting measures, initiating surge planning, and issuing public health advisories can benefit from approaches that allow state estimates for transmission models to be continuously updated in light of unfolding time series. A model being continuously regrounded by empirical data in this way can provide a consistent, integrated depiction of the evolving underlying epidemiology and acute care demand, offer the ability to project forward such a depiction in a fashion suitable for triggering the deployment of acute care surge capacity or public health measures, and support quantitative evaluation of tradeoffs associated with prospective interventions in light of the latest estimates of the underlying epidemiology. We describe here the design, implementation, and multi-year daily use for public health and clinical support decision-making of a particle-filtered COVID-19 compartmental model, which served Canadian federal and provincial governments via regular reporting starting in June 2020. The use of the Bayesian sequential Monte Carlo algorithm of particle filtering allows the model to be regrounded daily and adapt to new trends within daily incoming data-including test volumes and positivity rates, endogenous and travel-related cases, hospital census and admissions flows, daily counts of dose-specific vaccinations administered, measured concentration of SARS-CoV-2 in wastewater, and mortality. Important model outputs include estimates (via sampling) of the count of undiagnosed infectives, the count of individuals at different stages of the natural history of frankly and pauci-symptomatic infection, the current force of infection, effective reproductive number, and current and cumulative infection prevalence. Following a brief description of the model design, we describe how the machine learning algorithm of particle filtering is used to continually reground estimates of the dynamic model state, support a probabilistic model projection of epidemiology and health system capacity utilization and service demand, and probabilistically evaluate tradeoffs between potential intervention scenarios. We further note aspects of model use in practice as an effective reporting tool in a manner that is parameterized by jurisdiction, including the support of a scripting pipeline that permits a fully automated reporting pipeline other than security-restricted new data retrieval, including automated model deployment, data validity checks, and automatic post-scenario scripting and reporting. As demonstrated by this multi-year deployment of the Bayesian machine learning algorithm of particle filtering to provide industrial-strength reporting to inform public health decision-making across Canada, such methods offer strong support for evidence-based public health decision-making informed by ever-current articulated transmission models whose probabilistic state and parameter estimates are continually regrounded by diverse data streams.

Mathematical Modeling of Coccidiosis Dynamics in Chickens with Some Control Strategies

Coccidiosis is an infectious disease caused by the Eimeria species. The species can infect a bird’s digestive system, severely slow down its growth, and is a serious economic burden for chickens. A mathematical model for the transmission dynamics of coccidiosis disease in chickens in the presence of control interventions has been formulated and analyzed to gain insights into the dynamics of the disease in the population. Three control interventions, namely vaccination, sanitation, and treatment, are implemented. The study intends to assess the effects of these control interventions in coccidiosis transmission dynamics. Using the theory of differential equations, the invariant set of the model was derived, and the model’s solution was found to be mathematically and biologically significant. Analytical methods are employed to establish equilibrium solutions and investigate the stability of the model system’s equilibria, while numerical simulations illustrate the analytical results. The effective reproduction number is obtained using the next-generation matrix method, and the local stability of the equilibria of the model is established. The disease-free equilibrium is proved to be locally stable when the effective reproduction number is less than unity. Also, the nature of the bifurcation and its implications for disease prevention are investigated through the application of the center manifold theory. On the other hand, sensitivity analysis is carried out to investigate the parameters that impact the transmission of coccidiosis disease using the normalized forward sensitivity index. The parameters that have a greater influence on the effective reproduction number should be targeted for control purposes to lessen the spread of disease. Furthermore, numerical simulation is performed to investigate the contribution of each control intervention.

Natural experiments to assess the effectiveness of Covid-19 containment measures

To assess the effectiveness of non-pharmaceutical interventions (NPIs) in controlling infections during the Covid-19 pandemic, natural experiments are useful. This article introduces the principle of natural experiments and their statistical analysis and, in the first step, discusses their implementation in previous NPI studies. The validity of many studies on the effectiveness of NPIs is limited because, on the one hand, there are often no or only weak control conditions and, on the other hand, because there are problems in the specification of the analysis models. It is often implicitly assumed that only NPIs can slow down the infection process because there are no control variables for any other causes. In the second step, a natural experiment is analyzed about the effectiveness of five measures in the second Corona wave. Switzerland (where these measures were not taken) and neighboring Baden-Württemberg serve as comparison regions. It turns out that the closure of close-contact services causes a reduction in the effective reproduction number, i.e., dampens the wave of infections. However, closing schools and daycare facilities as well as hotels is not effective.

Public Health Impact of Paxlovid as Treatment for COVID-19, United States.

We evaluated the population-level benefits of expanding treatment with the antiviral drug Paxlovid (nirmatrelvir/ritonavir) in the United States for SARS-CoV-2 Omicron variant infections. Using a multiscale mathematical model, we found that treating 20% of symptomatic case-patients with Paxlovid over a period of 300 days beginning in January 2022 resulted in life and cost savings. In a low-transmission scenario (effective reproduction number of 1.2), this approach could avert 0.28 million (95% CI 0.03-0.59 million) hospitalizations and save US $56.95 billion (95% CI US $2.62-$122.63 billion). In a higher transmission scenario (effective reproduction number of 3), the benefits increase, potentially preventing 0.85 million (95% CI 0.36-1.38 million) hospitalizations and saving US $170.17 billion (95% CI US $60.49-$286.14 billion). Our findings suggest that timely and widespread use of Paxlovid could be an effective and economical approach to mitigate the effects of COVID-19.

SEI3R2D2V: Pandemic Modeling and Analysis of Its Latent Factors: A Case Study of COVID-19 in India

For densely populated developing countries, such as India, where due to a lack of general and public awareness, limited data collection and compilation facilities, and inherent limitations of the available diagnostic test, accurate modeling of the pandemic is more challenging. Thus, a realistic model for predictions is required in order to formulate more effective strategic policies to control the COVID-19 pandemic using limited available resources. In this article, we propose a time-varying epidemiological model with two classes of compartments, reported and unreported, and consider influential latent factors, for example, undetectable infections, the false-negative rate of testing, testing hesitancy, vaccination efficacy, dual contact dynamics, and the possibility of reinfection in recovered as well as vaccinated individuals. For simulation purposes, we consider the COVID-19 data of India from March 13, 2020, to January 20, 2022. Furthermore, we provide a sensitivity analysis of various latent factors and predictions for the third wave in India. Simulated results suggest that India is able to control COVID-19 for the first time after the second wave, as observed from the trajectory of effective reproduction number. Moreover, for unseen or coming variants of virus for which vaccine efficacy is low, the available vaccine requires a high vaccination rate to control future waves.

Supercritical and homogenous transmission of monkeypox in the capital of China.

Starting from May 31, 2023, the local transmission of monkeypox (Mpox) in mainland China began in Beijing. Till now, the transmission characteristics have not been explored. Based on the daily Mpox incidence data in the first 3 weeks of Beijing (from May 31 to June 21, 2023), we employed the instant-individual heterogeneity transmission model to simultaneously calculate the effective reproduction number (Re ) and the degree of heterogeneity (k) of the Beijing epidemic. We additionally simulated the monthly infection size in Beijing from July to November and compared with the reported data to project subsequent transmission dynamics. We estimated Re to be 1.68 (95% highest posterior density [HPD]: 1.12-2.41), and k to be 2.57 [95% HPD: 0.54-83.88], suggesting the transmission of Mpox in Beijing was supercritical and didn't have considerable transmission heterogeneity. We projected that Re fell in the range of 0.95-1.0 from July to November, highlighting more efforts needed to further reduce the Mpox transmissibility. Our findings revealed supercritical and homogeneous transmission of the Mpox epidemic in Beijing. Our results could serve as a reference for understanding and predicting the ongoing Mpox transmission in other regions of China and evaluating the effect of control measures.

Inferring community transmission of SARS-CoV-2 in the United Kingdom using the ONS COVID-19 Infection Survey

Key epidemiological parameters, including the effective reproduction number, R(t), and the instantaneous growth rate, r(t), generated from an ensemble of models, have been informing public health policy throughout the COVID-19 pandemic in the four nations of the United Kingdom of Great Britain and Northern Ireland (UK). However, estimation of these quantities became challenging with the scaling down of surveillance systems as part of the transition from the “emergency” to “endemic” phase of the pandemic.The Office for National Statistics (ONS) COVID-19 Infection Survey (CIS) provided an opportunity to continue estimating these parameters in the absence of other data streams. We used a penalised spline model fitted to the publicly-available ONS CIS test positivity estimates to produce a smoothed estimate of the prevalence of SARS-CoV-2 positivity over time. The resulting fitted curve was used to estimate the “ONS-based” R(t) and r(t) across the four nations of the UK. Estimates produced under this model are compared to government-published estimates with particular consideration given to the contribution that this single data stream can offer in the estimation of these parameters.Depending on the nation and parameter, we found that up to 77% of the variance in the government-published estimates can be explained by the ONS-based estimates, demonstrating the value of this singular data stream to track the epidemic in each of the four nations. We additionally find that the ONS-based estimates uncover epidemic trends earlier than the corresponding government-published estimates.Our work shows that the ONS CIS can be used to generate key COVID-19 epidemiological parameters across the four UK nations, further underlining the enormous value of such population-level studies of infection. This is not intended as an alternative to ensemble modelling, rather it is intended as a potential solution to the aforementioned challenge faced by public health officials in the UK in early 2022.

Rapid Spread of Omicron Sub-Lineage as Evidence by Wastewater Surveillance

The search for better tools for interpreting and understanding wastewater surveillance has continued since the beginning of the coronavirus disease 2019 (COVID-19) pandemic. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has continued to mutate, thus complicating the interpretation of surveillance results. We assessed the Omicron variants (BA.1, BA.2, and BA.5) associated with wastewater-derived SARS-CoV-2 RNA trends by estimating the effective reproduction number (Reff) using an epidemic model that integrates explicitly the SARS-CoV-2 N2 gene concentration detected in wastewater through rt-qPCR quantitative analysis. The model inferred COVID-19 cases based on wastewater data and compared them with the ones reported by clinical surveillance. The variant of the SARS-CoV-2 associated with the wastewater-derived viral RNA was monitored through wastewater whole-genome sequencing. Three major waves between January and September 2022 were associated with the Omicron subvariants (BA.1, BA.2, and BA.5). This work showed that disease trends can be monitored using estimates of the effective reproduction number which is simple and easy to understand.

Comparing the Performance of Three Computational Methods for Estimating the Effective Reproduction Number.

The effective reproduction number is one of the most important epidemiological parameters, providing suggestions for monitoring the development trend of diseases and also for adjusting the prevention and control policies. However, a few studies have focused on the performance of some common computational methods for Rt. The purpose of this article is to compare the performance of three computational methods for Rt: the time-dependent (TD) method, the new time-varying (NT) method, and the sequential Bayesian (SB) method. Four evaluation methods-accuracy, correlation coefficient, similarity based on trend, and dynamic time warping distance-were used to compare the effectiveness of three computational methods for Rt under different time lags and time windows. The results showed that the NT method was a better choice for real-time monitoring and analysis of the epidemic in the middle and late stages of the infectious disease. The TD method could reflect the change of the number of cases stably and accurately, and was more suitable for monitoring the change of Rt during the whole process of the epidemic outbreak. When the data were relatively stable, the SB method could also provide a reliable estimate for Rt, while the error would increase when the fluctuation in the number of cases increased. The results would provide suggestions for selecting appropriate Rt estimation methods and making policy adjustments more timely and effectively according to the change of Rt.

Assessment of vaccination and underreporting on COVID-19 infections in Turkey based on effective reproduction number

In this paper, we introduce a SEIR-type COVID-19 model where the infected class is further divided into subclasses with individuals in intensive care (ICUs) and ventilation units. The model is calibrated with the symptomatic COVID-19 cases, deaths, and the number of patients in ICUs and ventilation units as reported by Republic of Turkey, Ministry of Health for the period 11 March 2020 through 30 May 2020 when the nationwide lockdown is in order. COVID-19 interventions in Turkey are incorporated into the model to detect the future trend of the outbreak accurately. We tested the effect of underreporting and we found that the peaks of the disease differ significantly depending on the rate of underreporting, however, the timing of the peaks remains constant. The lockdown is lifted on 1 June, and the model is modified to include a time-dependent transmission rate which is linked to the effective reproduction number [Formula: see text] through basic reproduction number [Formula: see text]. The modified model captures the changing dynamics and peaks of the outbreak successfully. With the onset of vaccination on 13 January 2021, we augment the model with the vaccination class to investigate the impact of vaccination rate and efficacy. We observe that vaccination rate is a more critical parameter than the vaccine efficacy to eliminate the disease successfully.

Influenza transmission dynamics quantified from RNA in wastewater in Switzerland.

Influenza infections are challenging to monitor at the population level due to many mild and asymptomatic cases and similar symptoms to other common circulating respiratory diseases, including COVID-19. Methods for tracking cases outside of typical reporting infrastructure could improve monitoring of influenza transmission dynamics. Influenza shedding into wastewater represents a promising source of information where quantification is unbiased by testing or treatment-seeking behaviours. We quantified influenza A and B virus loads from influent at Switzerland's three largest wastewater treatment plants, serving about 14% of the Swiss population (1.2 million individuals). We estimated trends in infection incidence and the effective reproductive number (Re) in these catchments during a 2021/22 epidemic and compared our estimates to typical influenza surveillance data. Wastewater data captured the same overall trends in infection incidence as laboratory-confirmed case data at the catchment level. However, the wastewater data were more sensitive in capturing a transient peak in incidence in December 2021 than the case data. The Reestimated from the wastewater data was roughly at or below the epidemic threshold of 1 during work-from-home measures in December 2021 but increased to at or above the epidemic threshold in two of the three catchments after the relaxation of these measures. The third catchment yielded qualitatively the same results but with wider confidence intervals. The confirmed case data at the catchment level yielded comparatively less precise R_e estimates before and during the work-from-home period, with confidence intervals that included one before and during the work-from-home period. Overall, we show that influenza RNA in wastewater can help monitor nationwide influenza transmission dynamics. Based on this research, we developed an online dashboard for ongoing wastewater-based influenza surveillance in Switzerland.

Transmission chains of the first local outbreak cause by Delta VariantB.1.617.2 COVID-19 in Guangzhou, Southern China

BackgroundThe first local outbreak of Delta Variant B.1.617.2 COVID-19 of China occurred in Guangzhou city, south China, in May 2021. This study analyzed the transmission chains and local cluster characteristics of this outbreak, intended to provide information support for the development and adjustment of local prevention and control strategies.MethodsThe transmission chains and local cluster characteristics of 161 local cases in the outbreak were described and analyzed. Incubation period, serial interval and generation time were calculated using the exact time of exposure and symptom onset date of the cases. The daily number of reported cases and the estimated generation time were used to estimate the effective reproduction number (Rt).ResultsWe identified 7 superspreading events who had more than 5 next generation cases and their infected cases infected 70.81%(114/161) of all the cases transmission. Dining and family exposure were the main transmission routes in the outbreak, with 29.19% exposed through dining and 32.30% exposed through family places. Through further analysis of the outbreak, the estimated mean incubation period was 4.22 (95%CI: 3.66–4.94) days, the estimated mean generation time was 2.60 (95%CI: 1.96–3.11) days, and the estimated Rt was 3.29 (95%CI: 2.25–5.07).ConclusionsClassification and dynamically adjusted prevention and control measures had been carried out according to analysis of transmission chains and epidemical risk levels, including promoting nucleic acid screening at different regions and different risk levels, dividing closed-off area, controlled area according to the risk of infection, raising the requirements of leaving Guangzhou. By the above control measures, Guangzhou effectively control the outbreak within 28 days without implementing a large-scale lockdown policy.

Combining models to generate a consensus effective reproduction number R for the COVID-19 epidemic status in England

Abstract The effective reproduction number $ R $ was widely accepted as a key indicator during the early stages of the COVID-19 pandemic. In the UK, the $ R $ value published on the UK Government Dashboard has been generated as a combined value from an ensemble of epidemiological models via a collaborative initiative between academia and government. In this paper, we outline this collaborative modelling approach and illustrate how, by using an established combination method, a combined $ R $ estimate can be generated from an ensemble of epidemiological models. We analyse the $ R $ values calculated for the period between April 2021 and December 2021, to show that this $ R $ is robust to different model weighting methods and ensemble sizes and that using heterogeneous data sources for validation increases its robustness and reduces the biases and limitations associated with a single source of data. We discuss how $ R $ can be generated from different data sources and show that it is a good summary indicator of the current dynamics in an epidemic.

HIV incidence before and during the COVID-19 pandemic in Japan

<abstract> <p>At the end of 2022, a total of 20,003 diagnoses of human immunodeficiency virus (HIV) infection and 8,983 cases of acquired immunodeficiency syndrome (AIDS) among Japanese nationals, and 3,860 HIV diagnoses and 1,575 AIDS cases among foreign residents, had been notified to the government in Japan. This study updates the estimate of HIV incidence, including during the COVID-19 pandemic. It aimed to reconstruct the incidence of HIV and understand how the disruption caused by COVID-19 affected the epidemiology of HIV. Using a median incubation period of 10.0 years, the number of undiagnosed HIV infections was estimated to be 3,209 (95% confidence interval (CI): 2,642, 3,710) at the end of 2022. This figure has declined steadily over the past 10 years. Assuming that the median incubation period was 10.0 years, the proportion of diagnosed HIV infections, including surviving AIDS cases, was 89.3% (95% CI: 87.8%, 91.0%). When AIDS cases were excluded, the proportion was 86.2% (95% CI: 84.3%, 88.3%). During the COVID-19 pandemic, the estimated annual diagnosis rate was slightly lower than during earlier time intervals, at around 16.5% (95% CI: 14.9%, 18.1%). Japan may already have achieved diagnostic coverage of 90%, given its 9% increment in the diagnosed proportion during the past 5 years. The incidence of HIV infection continued to decrease even during the COVID-19 pandemic from 2020 to 2022, and the annual rate of diagnosis decreased slightly to 16.5%. Monitoring the recovery of diagnosis along with the effective reproduction number is vital in the future.</p> </abstract>

Comparative epidemiology of outbreaks caused by SARS-CoV-2 Delta and Omicron variants in China.

From 2020 to December 2022, China implemented strict measures to contain the spread of severe acute respiratory syndrome coronavirus 2. However, despite these efforts, sustained outbreaks of the Omicron variants occurred in 2022. We extracted COVID-19 case numbers from May 2021 to October 2022 to identify outbreaks of the Delta and Omicron variants in all provinces of mainland China. We found that omicron outbreaks were more frequent (4.3 vs. 1.6 outbreaks per month) and longer-lasting (mean duration: 13 vs. 4weeks per outbreak) than Delta outbreaks, resulting in a total of 865,100 cases, of which 85% were asymptomatic. Despite the average Government Response Index being 12% higher (95% confidence interval (CI): 9%, 15%) in Omicron outbreaks, the average daily effective reproduction number (Rt) was 0.45 higher (95% CI: 0.38, 0.52, p<0.001) than in Delta outbreaks. Omicron outbreaks were suppressed in 32days on average (95% CI: 26, 39), which was substantially longer than Delta outbreaks (14days; 95% CI: 11, 19; p=0.004). We concluded that control measures effective against Delta could not contain Omicron outbreaks in China. This highlights the need for continuous evaluation of new variants' epidemiology to inform COVID-19 response decisions.

Assessing the Time Evolution of COVID-19 Effective Reproduction Number in Brazil.

In this paper, we use a Bayesian method to estimate the effective reproduction number ( R ( t ) ), in the context of monitoring the time evolution of the COVID-19 pandemic in Brazil at different geographic levels. The focus of this study is to investigate the similarities between the trends in the evolution of such indicators at different subnational levels with the trends observed nationally. The underlying question addressed is whether national surveillance of such variables is enough to provide a picture of the epidemic evolution in the country or if it may hide important localized trends. This is particularly relevant in the scenario where health authorities use information obtained from such indicators in the design of non-pharmaceutical intervention policies to control the epidemic. A comparison between R ( t ) estimates and the moving average (MA) of daily reported infections is also presented, which is another commonly monitored variable. The analysis carried out in this paper is based on the data of confirmed infected cases provided by a public repository. The correlations between the time series of R ( t ) and MA in different geographic levels are assessed. Comparing national with subnational trends, higher degrees of correlation are found for the time series of R ( t ) estimates, compared to the MA time series. Nevertheless, differences between national and subnational trends are observed for both indicators, suggesting that local epidemiological surveillance would be more suitable as an input to the design of non-pharmaceutical intervention policies in Brazil, particularly for the least populated states.

Mathematical analysis and simulation of Ebola virus disease spread incorporating mitigation measures

In order to understand the dynamics of the Ebola virus disease (EVD), this research developed a mathematical model that includes quarantine and public education campaigns as control measures. The model’s equilibrium points are displayed and the effective basic reproduction number Reff is estimated. Bifurcation theory is used for the stability analysis of endemic equilibrium state and general bifurcation theory is used to prove the existence of endemic equilibrium state. We evaluated the nature of the endemic equilibrium state of the model’s equation near the disease-free equilibrium, Reff=1 and introduce a bifurcation parameter. The results of the centre manifold theory are used to demonstrate that there is nontrivial endemic equilibrium near the disease-free equilibrium. We demonstrated the characteristics of the endemic equilibrium state that is close to the disease-free equilibrium as well as the fact that there is a potentially unstable endemic equilibrium condition. In other words, the sickness is slowly declining and will eventually disappear, as in the case of West Africa. Finally, we simulated the model developed to study the dynamics of the diseases with varying parameters using Homotopy Perturbation Method (HPM) to validate the qualitative analysis of the model. The result confirmed the hypothesis of our research that if quarantine and public enlightenment is properly used for the mitigation of the disease, the disease outcomes will drastically reduced. The results presented in this research will be useful for public health experts to contain the Ebola disease spread most especially in Africa.

Optimal vaccination ages for emerging infectious diseases under limited vaccine supply.

Rational allocation of limited vaccine resources is one of the key issues in the prevention and control of emerging infectious diseases. An age-structured infectious disease model with limited vaccine resources is proposed to explore the optimal vaccination ages. The effective reproduction number [Formula: see text] of the epidemic disease is computed. It is shown that the reproduction number is the threshold value for eradicating disease in the sense that the disease-free steady state is globally stable if [Formula: see text] and there exists a unique endemic equilibrium if [Formula: see text]. The effective reproduction number is used as an objective to minimize the disease spread risk. Using the epidemic data from the early spread of Wuhan, China and demographic data of Wuhan, we figure out the strategies to distribute the vaccine to the age groups to achieve the optimal vaccination effects. These analyses are helpful to the design of vaccination schedules for emerging infectious diseases.

Predicting the transmission dynamics of novel coronavirus infection in Shanxi province after the implementation of the "Class B infectious disease Class B management" policy.

China managed coronavirus disease 2019 (COVID-19) with measures against Class B infectious diseases, instead of Class A infectious diseases, in a major shift of its epidemic response policies. We aimed to generate robust information on the transmission dynamics of novel coronavirus infection in Shanxi, a province located in northern China, after the implementation of the "Class B infectious disease Class B management" policy. We consolidated infection data in Shanxi province from December 6, 2022 to January 14, 2023 through a network questionnaire survey and sentinel surveillance. A dynamics model of the SEIQHCVR was developed to track the infection curves and effective reproduction number (). Our model was effective in estimating the trends of novel coronavirus infection, with the coefficient of determination () above 90% in infections, inpatients, and critically ill patients. The number of infections in Shanxi province as well as in urban and rural areas peaked on December 20, 2022, with the peak of inpatients and critically ill patients occurring 2 to 3 weeks after the peak of infections. By the end of January 2023, 87.72% of the Shanxi residents were predicted to be infected, and the outbreak subsequently subsided. A small wave of COVID-19 infections may re-emerge at the end of April. In less than a month, the values of positive infections, inpatients and critically ill patients were all below 1.0. The outbreak in Shanxi province is currently at a low prevalence level. In the face of possible future waves of infection, there is a strong need to strengthen surveillance and early warning.

Optimal control strategies on HIV/AIDS and pneumonia co-infection with mathematical modelling approach

In this paper, a compartmental model on the co-infection of pneumonia and HIV/AIDS with optimal control strategies was formulated using the system of ordinary differential equations. Using qualitative methods, we have analysed the mono-infection and HIV/AIDS and pneumonia co-infection models. We have computed effective reproduction numbers by applying the next-generation matrix method, applying Castillo Chavez criteria the models disease-free equilibrium points global stabilities were shown, while we have used the Centre manifold criteria to determine that the pneumonia infection and pneumonia and HIV/AIDS co-infection exhibit the phenomenon of backward bifurcation whenever the corresponding effective reproduction number is less than unity. We carried out the numerical simulations to investigate the behaviour of the co-infection model solutions. Furthermore, we have investigated various optimal control strategies to predict the best control strategy to minimize and possibly to eradicate the HIV/AIDS and pneumonia co-infection from the community.